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 H W A Riaz;J Lin

作者机构：Department of PhysicsZhejiang Normal UniversityJinhua 321004China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2024年第76卷第3期

页      面：51-61页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：integrable systems Darboux transformation solitons 

摘      要：The nonlinear Schr?dinger(NLS)equation,which incorporates higher-order dispersive terms,is widely employed in the theoretical analysis of various physical *** this study,we explore the non-commutative extension of the higher-order NLS *** 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 *** derive the quasi-Gramian solution of the system by employing a binary Darboux *** soliton solutions are presented explicitly within the framework of *** visually understand the dynamics and solutions in the given example,we also provide simulations illustrating the associated ***,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.