Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations  

作　　者：Alemu Yilma Tefera Shangshuai Li Da-jun Zhang 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China [2]Newtouch Center for Mathematics of Shanghai University,Shanghai 200444,China [3]Department of Applied Mathematics,Faculty of Science and Engineering,Waseda University,Tokyo 169-8555,Japan

出　　处：《Communications in Theoretical Physics》2024年第5期1-15,共15页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12271334).

摘　　要：This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

关 键 词：Cauchy matrix approach Sylvester equation nonlinear Schrödinger equation non-isospectral integrable system explicit solution 

分 类 号：O175.29[理学—数学]