We consider the scattering of Cauchy problem for the focusing combined power-type Schroodinger equation. In the spirit of concentration-compactness method, we will show that, H1 solution will scatter under some condit...We consider the scattering of Cauchy problem for the focusing combined power-type Schroodinger equation. In the spirit of concentration-compactness method, we will show that, H1 solution will scatter under some condition on its energy and mass. We adapt some variance argument, following the idea of Ibrahim–Masmoudi–Nakanishi.展开更多
In the paper,we want to derive a few of nonlinear Schrodinger equations with various formats and investigate their properties,such as symmetries,single soliton solutions,multi-soliton solutions,and so on.First of all,...In the paper,we want to derive a few of nonlinear Schrodinger equations with various formats and investigate their properties,such as symmetries,single soliton solutions,multi-soliton solutions,and so on.First of all,we propose an efficient and straightforward scheme for generating nonisospectral integrable hierarchies of evolution equations for which a generalized nonisospectral integrable Schrodinger hierarchy(briefly GNISH)singles out,from which we get a derivative nonlinear Schrodinger equation,a generalized nonlocal Schrodinger integrable system and furthermore we investigate the symmetries and conserved qualities of the GNISH.Next,we apply the dbar method to obtain a generalized nonlinear Schr?dinger-Maxwell-Bloch(GNLS-MB)equation and its hierarchy by introducing a generalized Zakhrov-Shabat spectral problem,whose soliton solutions and gauge transformations are obtained.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11226184,11226065,11271322 and11271105)
文摘We consider the scattering of Cauchy problem for the focusing combined power-type Schroodinger equation. In the spirit of concentration-compactness method, we will show that, H1 solution will scatter under some condition on its energy and mass. We adapt some variance argument, following the idea of Ibrahim–Masmoudi–Nakanishi.
基金supported by the National Natural Science Foundation of China(No.11971475)。
文摘In the paper,we want to derive a few of nonlinear Schrodinger equations with various formats and investigate their properties,such as symmetries,single soliton solutions,multi-soliton solutions,and so on.First of all,we propose an efficient and straightforward scheme for generating nonisospectral integrable hierarchies of evolution equations for which a generalized nonisospectral integrable Schrodinger hierarchy(briefly GNISH)singles out,from which we get a derivative nonlinear Schrodinger equation,a generalized nonlocal Schrodinger integrable system and furthermore we investigate the symmetries and conserved qualities of the GNISH.Next,we apply the dbar method to obtain a generalized nonlinear Schr?dinger-Maxwell-Bloch(GNLS-MB)equation and its hierarchy by introducing a generalized Zakhrov-Shabat spectral problem,whose soliton solutions and gauge transformations are obtained.
