The quasi-Gramian solution of a non-commutative extension of the higher-order nonlinear Schr?dinger equation  

作　　者：H W A Riaz J Lin 

机构地区：[1]Department of Physics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Communications in Theoretical Physics》2024年第3期51-61,共11页理论物理通讯（英文版）

基　　金：the support from the National Natural Science Foundation of China,Nos.11835011 and 12375006。

摘　　要：The nonlinear Schr?dinger(NLS)equation,which incorporates higher-order dispersive terms,is widely employed in the theoretical analysis of various physical phenomena.In this study,we explore the non-commutative extension of the higher-order NLS equation.We treat real or complex-valued functions,such as g_(1)=g_(1)(x,t)and g_(2)=g_(2)(x,t)as non-commutative,and employ the Lax pair associated with the evolution equation,as in the commutation case.We derive the quasi-Gramian solution of the system by employing a binary Darboux transformation.The soliton solutions are presented explicitly within the framework of quasideterminants.To visually understand the dynamics and solutions in the given example,we also provide simulations illustrating the associated profiles.Moreover,the solution can be used to study the stability of plane waves and to understand the generation of periodic patterns within the context of modulational instability.

关 键 词：integrable systems Darboux transformation SOLITONS 

分 类 号：O411.1[理学—理论物理]