In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the ...In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.展开更多
So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. Bu...So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.展开更多
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi...Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.展开更多
The nonlinear Schrodinger equation is proved to be consistent-tanh-expansion （CTE） solvable. Some types of dark soliton solutions dressed by cnoidal periodic waves are obtained by means of the CTE method.
Many sets of the soliton and periodic travelling wave solutions for the quadratic χ^（2） nonlinear system are obtained by the Backlund transformation and the trial method. The property of the propagation for some tr...Many sets of the soliton and periodic travelling wave solutions for the quadratic χ^（2） nonlinear system are obtained by the Backlund transformation and the trial method. The property of the propagation for some travelling waves is investigated.展开更多
We extend the method of constructing Bgcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized v...We extend the method of constructing Bgcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg-de Vries （KdV） equations as examples, their Backlund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Es- pecially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.展开更多
We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota b...We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.展开更多
Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equa...Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures.By introducing the velocity resonance mechanism to the multiple kink solutions,we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients.The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited.After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada-Kotera-Caudrey-Dodd-Gibbons(SKCDG)equation,the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10575087） and the Natural Science Foundation of Zheiiang Province of China （Grant No 102053）. 0ne of the authors （Lin） would like to thank Prof. Sen-yue Lou for many useful discussions.
文摘In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106)
文摘So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11505154,11605156,11775146,and 11975204)the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ16A010003 and LY19A050003)+5 种基金the China Scholarship Council(Grant No.201708330479)the Foundation for Doctoral Program of Zhejiang Ocean University(Grant No.Q1511)the Natural Science Foundation(Grant No.DMS-1664561)the Distinguished Professorships by Shanghai University of Electric Power(China)North-West University(South Africa)King Abdulaziz University(Saudi Arabia)
文摘Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.
基金Sponsored by the National Natural Science Foundation of China under Grant Nos 11175092, 11275123, 11205092 and 10905038, the Scientific Research Fund of Zhejiang-Provincial Education Department under Grant No Y201017148, and the K. C. Wong Magna Fund in Ningbo University.
文摘The nonlinear Schrodinger equation is proved to be consistent-tanh-expansion （CTE） solvable. Some types of dark soliton solutions dressed by cnoidal periodic waves are obtained by means of the CTE method.
基金Supported by the National 0utstanding Youth Foundation of China under No 19925522, the National Natural Science Foundation of China under Nos 90203001 and 10575087, and the Natural Science Foundation of Zhejiang Province of China under Grant No 102053.
文摘Many sets of the soliton and periodic travelling wave solutions for the quadratic χ^（2） nonlinear system are obtained by the Backlund transformation and the trial method. The property of the propagation for some travelling waves is investigated.
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ12A01008 and LY12A01010)
文摘We extend the method of constructing Bgcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg-de Vries （KdV） equations as examples, their Backlund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Es- pecially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.
基金supported by the National Natural Science Foundation of China (Grant Nos.11975204 and 12075208)the Project of Zhoushan City Science and Technology Bureau (Grant No.2021C21015)the Training Program for Leading Talents in Universities of Zhejiang Province。
文摘We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.
基金the National Natural Science Foundation of China(Grant Nos.11975204,11835011,and 12075208)the Natural Science Foundation of Zhejiang Province(Grant No.LY19A050003)the Project of Zhoushan City Science and Technology Bureau(Grant No.2021C21015)。
文摘Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures.By introducing the velocity resonance mechanism to the multiple kink solutions,we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients.The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited.After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada-Kotera-Caudrey-Dodd-Gibbons(SKCDG)equation,the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.
