It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approx...It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.展开更多
This work focuses on the evolution behaviors of ring dark solitons(RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose–Einstein condensates. We find that the weighted average of the initial de...This work focuses on the evolution behaviors of ring dark solitons(RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose–Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis.For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally.Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.展开更多
The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the pertu...The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.展开更多
The weak Darboux transformation of the （2＋1） dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as ...The weak Darboux transformation of the （2＋1） dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as the Rossby waves can be simply obtained from the weak Darboux transformation with zero spectral parameters. The constant vorticity seed solution is utilized to generate Bessel waves.展开更多
Approximate generalized conditional symmetry is developed to study the approximate symmetry reduction for initial-value problems of the extended KdV-Burgers equations with perturbation.These equations can be reduced t...Approximate generalized conditional symmetry is developed to study the approximate symmetry reduction for initial-value problems of the extended KdV-Burgers equations with perturbation.These equations can be reduced to initial-value problems for some systems of first-order perturbed ordinary differential equations in terms of a new approach.Complete classification theorems are obtained and an example is taken to show the main reduction procedure.展开更多
The structural and electronic properties of monovacancy,divacancy defects within crystalline silicon have been investigated systematically using a new tight-binding model with a 216-atom supercell.The formation energi...The structural and electronic properties of monovacancy,divacancy defects within crystalline silicon have been investigated systematically using a new tight-binding model with a 216-atom supercell.The formation energies and energy levels of all the defect configurations are carefully calculated.The results show that atoms nearer to the defects naturally contribute to gap states more,and are comparable with the experimental values.展开更多
The three most widely used methods for reconstructing the underlying time series via the recurrence plots （RPs） of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a...The three most widely used methods for reconstructing the underlying time series via the recurrence plots （RPs） of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.展开更多
By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from ...By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.展开更多
The functional variable separation approach is applied to study extended （1＋2）-dimensional nonlinear wave equations. Complete classification for those equations admitting the functional separable solutions and some...The functional variable separation approach is applied to study extended （1＋2）-dimensional nonlinear wave equations. Complete classification for those equations admitting the functional separable solutions and some exact separable solutions are obtained.展开更多
We use the latest baryon acoustic oscillation and Union 2.1 type Ia supernova data to test the cosmic opacity between different redshift regions without assuming any cosmological models. It is found that the universe ...We use the latest baryon acoustic oscillation and Union 2.1 type Ia supernova data to test the cosmic opacity between different redshift regions without assuming any cosmological models. It is found that the universe may be opaque between the redshift regions 0.35 0.44, 0.44 0.57 and 0.6-0.73 since the best fit values of cosmic opacity in these regions are positive, while a transparent universe is favored in the redshift region 0.57-0.63. However, in general, a transparent universe is still consistent with observations at the lo confidence level.展开更多
A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical ...A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a diploe blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research （NCEP/NCAR） reanalysis data is well described by the analytical solution.展开更多
In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for ...In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for surjective maps between groups of positive continuousfunctions to be a composition operator.展开更多
The propagators of quantum chaotic systems in configuration space are calculated semiclassically. For the strongly chaotic system whose phase space is torus, such as baker's map, we find that, long after a logarit...The propagators of quantum chaotic systems in configuration space are calculated semiclassically. For the strongly chaotic system whose phase space is torus, such as baker's map, we find that, long after a logarithm time, the quantum propagator can be evaluated approximately as the local average of the semiclassical one on each quantum cell h.展开更多
In this paper,a derivation of the macroscopic mean field theory of the cellular automaton(CA)model of highway traffic flow starting from the microscopic dynamical point of view is presented.Starting from an equation d...In this paper,a derivation of the macroscopic mean field theory of the cellular automaton(CA)model of highway traffic flow starting from the microscopic dynamical point of view is presented.Starting from an equation describing the time evolution of the Boolean state variable at each site of the basic CA model,and using a two-site approximation for the multi-site correlation functions,a dynamical mapping between the macroscopic average speeds v(t+1)and v(t)at different time can be derived.Mean field results consistent with the simulation data are obtained by considering the attractors of the mapping and their corresponding basins.展开更多
This work focuses on chirped solitons in a higher-order nonlinear Schrodinger equation,including cubic-quinticseptic nonlinearity,weak nonlocal nonlinearity,self-frequency shift,and self-steepening effect.For the firs...This work focuses on chirped solitons in a higher-order nonlinear Schrodinger equation,including cubic-quinticseptic nonlinearity,weak nonlocal nonlinearity,self-frequency shift,and self-steepening effect.For the first time,analytical bright and kink solitons,as well as their corresponding chirping,are obtained.The influence of septic nonlinearity and weak nonlocality on the dynamical behaviors of those nonlinearly chirped solitons is thoroughly addressed.The findings of the study give an experimental basis for nonlinear-managed solitons in optical fibers.展开更多
We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are ...We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are obtained. The simulation results show that the linear seed length has little effect on the pattern structure of the aggregation clusters if its length is comparatively shorter. With its increasing, the linear seed length has stronger effects on the pattern structure, while the dimension D f decreases. When the linear seed length is larger, the corresponding pattern structure is cross alike. The larger the linear seed length is, the more obvious the cross-like structure with more particles clustering at the two ends of the linear seed and along the vertical direction to the centre of the linear seed. Furthermore, the multifractal spectra curve becomes lower and the range of singularity narrower. The longer the length of a linear seed is, the less irregular and nonuniform the pattern becomes.展开更多
Using a special solution of the Euler equation, the relation between the position of the typhoon centre and the induced flow （background wind） is found. The relation can be used to predict the typhoon track. The pre...Using a special solution of the Euler equation, the relation between the position of the typhoon centre and the induced flow （background wind） is found. The relation can be used to predict the typhoon track. The prediction of the track for No 1 tropical cyclone, CHANCHU, is concretely provided.展开更多
We present a novel approach for generating stable three-dimensional(3D)spatiotemporal solitons(SSs)within a rotating Bose–Einstein condensate,incorporating spin–orbit coupling(SOC),a weakly anharmonic potential and ...We present a novel approach for generating stable three-dimensional(3D)spatiotemporal solitons(SSs)within a rotating Bose–Einstein condensate,incorporating spin–orbit coupling(SOC),a weakly anharmonic potential and cold Rydberg atoms.This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges|m|≤3 in two spinor components,potentially exhibiting diverse spatial configurations.Our findings reveal that the Rydberg long-range interaction,spin–orbit coupling,and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons.Notably,the Rydberg interaction contributes to a reduction in the norm of topological solitons,while the SOC plays a key role in stabilizing the SSs with finite topological charges.This research of SSs exhibits potential applications in precision measurement,quantum information processing,and other advanced technologies.展开更多
Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems ...Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science.In this paper,the associated network family of the unified piecewise-linear(PWL)chaotic family,which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system,was firstly constructed and analyzed.We constructed the associated network family via the original and the modified frequency-degree mapping strategy,as well as the classical visibility graph and horizontal visibility graph strategy,after removing the transient states.Typical related network characteristics,including the network fractal dimension,of the associated network family,are computed with changes of single key parameter a.These characteristic vectors of the network are also compared with the largest Lyapunov exponent(LLE)vector of the related original dynamical system.It can be found that,some network characteristics are highly correlated with LLE vector of the original nonlinear system,i.e.,there is an internal consistency between the largest Lyapunov exponents,some typical associated network characteristics,and the related network fractal dimension index.Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation,which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.展开更多
We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equ...We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equations. The obtained reductions cannot be derived within the framework of the standard Lie approach.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11175092)Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y201017148)K.C.Wong Magna Fund in Ningbo University
文摘It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.
基金supported by the National Natural Science Foundation of China (Grant Nos.12261131495,11975172,and 12381240286)。
文摘This work focuses on the evolution behaviors of ring dark solitons(RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose–Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis.For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally.Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10371098 and 10447007, the Natural Science Foundation of Shaanxi Province （No 2005A13）, and the Special Research Project of Educational Department of Shaanxi Province （No 03JK060）.
文摘The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90203001, 10475055 and 90503006.
文摘The weak Darboux transformation of the （2＋1） dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as the Rossby waves can be simply obtained from the weak Darboux transformation with zero spectral parameters. The constant vorticity seed solution is utilized to generate Bessel waves.
基金Supported by the National Natural Science Foundation of China under Grant No 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No SJ08A05the NWU Graduate Innovation and Creativity Funds(09YZZ56)。
文摘Approximate generalized conditional symmetry is developed to study the approximate symmetry reduction for initial-value problems of the extended KdV-Burgers equations with perturbation.These equations can be reduced to initial-value problems for some systems of first-order perturbed ordinary differential equations in terms of a new approach.Complete classification theorems are obtained and an example is taken to show the main reduction procedure.
基金Supported by the National Natural Science Foundation of China under Grant No.69876035,the Fund of Chinese Academy of Sciences and the Fund of University of Science and Technology of China.
文摘The structural and electronic properties of monovacancy,divacancy defects within crystalline silicon have been investigated systematically using a new tight-binding model with a 216-atom supercell.The formation energies and energy levels of all the defect configurations are carefully calculated.The results show that atoms nearer to the defects naturally contribute to gap states more,and are comparable with the experimental values.
基金Project supported by the Key Project of Ministry of Education of China (Grant No. 2010141)the National Natural Science Foundation of China (Grant No. 61203159)
文摘The three most widely used methods for reconstructing the underlying time series via the recurrence plots （RPs） of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.
基金Supported by the Outstanding Youth Foundationthe National Natural Science Foundation of Chinathe Doctoral Program of Higher Education.
文摘By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10371098, 10447007 and 10475055, the Special Research Project of Educational Department of Shaanxi Province （No 03JK060）.
文摘The functional variable separation approach is applied to study extended （1＋2）-dimensional nonlinear wave equations. Complete classification for those equations admitting the functional separable solutions and some exact separable solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175093,11222545,11435006 and 11375092the K.C.Wong Magna Fund of Ningbo University
文摘We use the latest baryon acoustic oscillation and Union 2.1 type Ia supernova data to test the cosmic opacity between different redshift regions without assuming any cosmological models. It is found that the universe may be opaque between the redshift regions 0.35 0.44, 0.44 0.57 and 0.6-0.73 since the best fit values of cosmic opacity in these regions are positive, while a transparent universe is favored in the redshift region 0.57-0.63. However, in general, a transparent universe is still consistent with observations at the lo confidence level.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90203001, 10475055, 10547124 and 40305009.
文摘A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a diploe blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research （NCEP/NCAR） reanalysis data is well described by the analytical solution.
基金supported in part by the NSFC(11671314)the Foundation of Hubei Provincial Department of Education(Q20161602)+1 种基金supported in part by the NSF-DMS(1200370)the NSFC(11628102)
文摘In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for surjective maps between groups of positive continuousfunctions to be a composition operator.
文摘The propagators of quantum chaotic systems in configuration space are calculated semiclassically. For the strongly chaotic system whose phase space is torus, such as baker's map, we find that, long after a logarithm time, the quantum propagator can be evaluated approximately as the local average of the semiclassical one on each quantum cell h.
基金Supported by the Chinese National Basic Research Project"Nonlinear Science"the National Natural Science Foundation of China under Grant No.49474216the Science Foundation of Shanghai on Traffic Problem Research.
文摘In this paper,a derivation of the macroscopic mean field theory of the cellular automaton(CA)model of highway traffic flow starting from the microscopic dynamical point of view is presented.Starting from an equation describing the time evolution of the Boolean state variable at each site of the basic CA model,and using a two-site approximation for the multi-site correlation functions,a dynamical mapping between the macroscopic average speeds v(t+1)and v(t)at different time can be derived.Mean field results consistent with the simulation data are obtained by considering the attractors of the mapping and their corresponding basins.
基金supported by the National Natural Science Foundation of China(Grant No.11975172)the Science and Technology Plan of Shenzhen City(Grant Nos.JCYJ20180306173235924 and JCYJ20180305164708625)。
文摘This work focuses on chirped solitons in a higher-order nonlinear Schrodinger equation,including cubic-quinticseptic nonlinearity,weak nonlocal nonlinearity,self-frequency shift,and self-steepening effect.For the first time,analytical bright and kink solitons,as well as their corresponding chirping,are obtained.The influence of septic nonlinearity and weak nonlocality on the dynamical behaviors of those nonlinearly chirped solitons is thoroughly addressed.The findings of the study give an experimental basis for nonlinear-managed solitons in optical fibers.
基金Supported by the Natural Science Foundation of Wuhan University of Science and Engineering under Grant No 20063133, and the Natural Science Foundation of Hubei Province under Grant No 2003ABA057.
文摘We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are obtained. The simulation results show that the linear seed length has little effect on the pattern structure of the aggregation clusters if its length is comparatively shorter. With its increasing, the linear seed length has stronger effects on the pattern structure, while the dimension D f decreases. When the linear seed length is larger, the corresponding pattern structure is cross alike. The larger the linear seed length is, the more obvious the cross-like structure with more particles clustering at the two ends of the linear seed and along the vertical direction to the centre of the linear seed. Furthermore, the multifractal spectra curve becomes lower and the range of singularity narrower. The longer the length of a linear seed is, the less irregular and nonuniform the pattern becomes.
基金Supported by the National Natural Science Foundation of China under Grant Nos 40305099 and 10475055.
文摘Using a special solution of the Euler equation, the relation between the position of the typhoon centre and the induced flow （background wind） is found. The relation can be used to predict the typhoon track. The prediction of the track for No 1 tropical cyclone, CHANCHU, is concretely provided.
基金supported by the National Natural Science Foundation of China(Grant Nos.62275075 and 11975172)the Sci-ence and Technology Research Program of Education De-partment of Hubei Province(Grant No.B2022188)+1 种基金the Natural Science Foundation of Hubei Province(Grant No.2023AFC042)the Training Program of Innova-tion and Entrepreneurship for Undergraduates of Hubei Province(Grant No.S202210927003).
文摘We present a novel approach for generating stable three-dimensional(3D)spatiotemporal solitons(SSs)within a rotating Bose–Einstein condensate,incorporating spin–orbit coupling(SOC),a weakly anharmonic potential and cold Rydberg atoms.This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges|m|≤3 in two spinor components,potentially exhibiting diverse spatial configurations.Our findings reveal that the Rydberg long-range interaction,spin–orbit coupling,and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons.Notably,the Rydberg interaction contributes to a reduction in the norm of topological solitons,while the SOC plays a key role in stabilizing the SSs with finite topological charges.This research of SSs exhibits potential applications in precision measurement,quantum information processing,and other advanced technologies.
文摘Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science.In this paper,the associated network family of the unified piecewise-linear(PWL)chaotic family,which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system,was firstly constructed and analyzed.We constructed the associated network family via the original and the modified frequency-degree mapping strategy,as well as the classical visibility graph and horizontal visibility graph strategy,after removing the transient states.Typical related network characteristics,including the network fractal dimension,of the associated network family,are computed with changes of single key parameter a.These characteristic vectors of the network are also compared with the largest Lyapunov exponent(LLE)vector of the related original dynamical system.It can be found that,some network characteristics are highly correlated with LLE vector of the original nonlinear system,i.e.,there is an internal consistency between the largest Lyapunov exponents,some typical associated network characteristics,and the related network fractal dimension index.Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation,which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.
基金Supported by the National Natural Science Foundation of China under Grant No 10447007, and the Natural Science Foundation of Shaanxi Province under Grant No 2005A13.
文摘We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equations. The obtained reductions cannot be derived within the framework of the standard Lie approach.
