In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise....In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
In this paper, the generalized synchronization of two unidirectionally coupled Ginzburg Landau equations is studied theoretically. It is demonstrated that the drive-response system has bounded attraction domain and co...In this paper, the generalized synchronization of two unidirectionally coupled Ginzburg Landau equations is studied theoretically. It is demonstrated that the drive-response system has bounded attraction domain and compact attractors. It is derived that the correction equation has asymptotically stable zero solutions under certain conditions and that the sufficient conditions for smooth generalized synchronization and Holder continuous generalized synchronization exist in the coupling system. Numerical result analysis shows the correctness of theory.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ...In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.展开更多
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge t...Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.展开更多
In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzent...In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.展开更多
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio...By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solv...In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.展开更多
The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized ...The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.展开更多
This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete mu...This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.展开更多
This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a n...This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.展开更多
It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. M...It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. Meanwhile it is obtained the solution is exponential decay when the initial data has compact support.展开更多
Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solut...Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.展开更多
In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics ...In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions, one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results, some previous one- and two- soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one- and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.展开更多
In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the unique...In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.展开更多
This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial f...In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.展开更多
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金Project supported by the Fundamental Research Funds for the Central Universities (Grant No. JUSRP211A21)the National Natural Science Foundation of China (Grant No. 11002061)
文摘In this paper, the generalized synchronization of two unidirectionally coupled Ginzburg Landau equations is studied theoretically. It is demonstrated that the drive-response system has bounded attraction domain and compact attractors. It is derived that the correction equation has asymptotically stable zero solutions under certain conditions and that the sufficient conditions for smooth generalized synchronization and Holder continuous generalized synchronization exist in the coupling system. Numerical result analysis shows the correctness of theory.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
文摘In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12326305,11931017,and 12271490)the Excellent Youth Science Fund Project of Henan Province(Grant No.242300421158)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia Autonomous Region, Natural Science Foundation of Inner Mongolia Autonomous Region （Grant No 2004080201103） and the Youth Research Program of Inner Mongolia Normal University （Grant No QN005023）.
文摘In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.
基金Project supported by the State Key Program for Basic Research of China (Grant No 2004CB418304)the National Natural Science Foundation of China (Grant No 40405010)
文摘By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
基金supported by National Natural Science Foundation of China (10571047)and by Scientific Research Fund of Hunan Provincial Education Department of China Grant(06C235)+1 种基金by Central South University of Forestry and Technology (06Y017)by Specialized Research Fund for the Doctoral Program of Higher Education (20060532014)
文摘In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(Grant No.KYLX16-0414)
文摘The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572119, 10772147 and 10632030)the Doctoral Program Foundation of Education Ministry of China (Grant No 20070699028)+1 种基金the National Natural Science Foundation of Shaanxi Province of China (Grant No 2006A07)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment
文摘This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)
文摘This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.
文摘It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. Meanwhile it is obtained the solution is exponential decay when the initial data has compact support.
文摘Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.
基金supported by the Natural Science Foundations of Zhejiang Province of China (Grant No. Y6090592)the National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030)+1 种基金Ningbo Natural Science Foundation (Grant Nos.2010A610095,2010A610103 and 2009B21003)K.C. Wong Magna Fund in Ningbo University
文摘In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions, one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results, some previous one- and two- soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one- and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.
基金supported by the National Natural Science Foundation of China(11226175,11271336 and 11171311)Specialized Reseach Fund for the Docotoral Program of Higher Education(20124301120002)Foundation of He’nan Educational Committee(2009C110006)
文摘In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
基金Project supported in part by the National Natural Science Foundation of China(Grant No.11071177)
文摘In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.
