多分量非线性可积系统中的奇异局域矢量波  

Exotic localized vector waves in the multicomponent nonlinear integrable systems

作　　者：王秀彬 陈勇[1] 韩波[1] 田守富 Wang Xiu-Bin;Chen Yong;Han Bo;Tian Shou-Fu

机构地区：[1]哈尔滨工业大学数学学院,哈尔滨150001 [2]中国矿业大学数学学院,徐州221116

出　　处：《中国科学：数学》2022年第9期1057-1072,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871180和11975306)资助项目。

摘　　要：本文利用Darboux变换结合渐近展开方法推导出多分量非局部非线性Schrodinger方程的一般高阶有理解.当参数满足特定的约束条件时,本文利用一些图形详细地讨论了非局部系统解的动力学行为.这些结果表明多分量非局部系统中存在更丰富的局域波结构.更重要的是,所得结果也可用于解释非局部波模型中相应的波现象.In this paper,general higher-order rational solutions of the nonlocal multicomponent nonlinear Schrodinger equations are derived by using a method of Darboux-dressing transformation with an asymptotic expansion.When the free parameters satisfy some constraints,the dynamics of those solutions in the nonlocal systems are discussed with some graphics.They demonstrate that the structure of localized waves in this multicomponent nonlocal system is richer than that in a one-component nonlocal system.More importantly,the results may be useful to explain and enrich the corresponding wave phenomena in local wave models.

关 键 词：可积系统 DARBOUX变换 变量分离技术 孤子 

分 类 号：O175[理学—数学]