Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for...The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.展开更多
A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using su...A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.展开更多
We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by usin...We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.展开更多
Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transforma...Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.展开更多
With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction,...With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.展开更多
The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstl...The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.展开更多
In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the inva...In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.展开更多
In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of...In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.展开更多
文摘Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
文摘The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.
基金UGC,New Delhi,India under the Special Assistance Programme DSA Phase-1
文摘A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.
文摘We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10772110） and the Natural Science Foundation of Zhejiang Province, China （Grant Nos. Y606049, Y6090681, and Y6100257）.
文摘Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
基金Project supported by the National Natural Science Foundations of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers (Grant No. 2009RC01)the Scientific Research and Developed Fund of Zhejiang Agricultural and Forestry University,China (Grant No. 2009FK42)
文摘With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11874324 and 11705164)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY17A040011,LY17F050011,and LR20A050001)+1 种基金the Foundation of “New Century 151 Talent Engineering” of Zhejiang Province of Chinathe Youth Talent Program of Zhejiang A&F University
文摘The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.
文摘In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.
基金Project supported by the Scientific Research Foundation of Lishui University,China (Grant No. KZ201110)
文摘In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.
