We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localiz...We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.展开更多
In this paper, coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations with variable coefficients are studied, which can be used to describe the interaction amon...In this paper, coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations with variable coefficients are studied, which can be used to describe the interaction among the modes in nonlinear optics and Bose-Einstein condensation. Some novel bright-dark solitons and dark-dark solitons are obtained by modified Sine-Gordon equation method. Moreover, some figures are provided to illustrate how the soliton solutions propagation is determined by the different values of the variable group velocity dispersion terms, which can be used to model various phenomena.展开更多
In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinat...In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinate system for quantum particle in cylindrical can. All elementary functions and most of the special functions which are the solution of extensive problems in physics and engineering are special cases of Meijer’s G-functions.展开更多
In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact e...In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11871232 and 12201578)Natural Science Foundation of Henan Province,China(Grant Nos.222300420377 and 212300410417)。
文摘We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.
文摘In this paper, coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations with variable coefficients are studied, which can be used to describe the interaction among the modes in nonlinear optics and Bose-Einstein condensation. Some novel bright-dark solitons and dark-dark solitons are obtained by modified Sine-Gordon equation method. Moreover, some figures are provided to illustrate how the soliton solutions propagation is determined by the different values of the variable group velocity dispersion terms, which can be used to model various phenomena.
文摘In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinate system for quantum particle in cylindrical can. All elementary functions and most of the special functions which are the solution of extensive problems in physics and engineering are special cases of Meijer’s G-functions.
文摘In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.
