In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All s...In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation.展开更多
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 extensi...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.展开更多
Using a quasideterminant Darboux matrix, we compute soliton solutions of a negative order AKNS(AKNS(-1)) equation.Darboux transformation(DT) is defined on the solutions to the Lax pair and the AKNS(-1)equation.By iter...Using a quasideterminant Darboux matrix, we compute soliton solutions of a negative order AKNS(AKNS(-1)) equation.Darboux transformation(DT) is defined on the solutions to the Lax pair and the AKNS(-1)equation.By iterated DT to K-times, we obtain multisoliton solutions.It has been shown that multisoliton solutions can be expressed in terms of quasideterminants and shown to be related with the dressed solutions as obtained by dressing method.展开更多
文摘In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation.
基金the support from the National Natural Science Foundation of China,Nos.11835011 and 12375006。
文摘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.
文摘Using a quasideterminant Darboux matrix, we compute soliton solutions of a negative order AKNS(AKNS(-1)) equation.Darboux transformation(DT) is defined on the solutions to the Lax pair and the AKNS(-1)equation.By iterated DT to K-times, we obtain multisoliton solutions.It has been shown that multisoliton solutions can be expressed in terms of quasideterminants and shown to be related with the dressed solutions as obtained by dressing method.
