Abstract
In this paper, we investigate an integrable high order nonlocal coupled Ablowitz-Kaup-Newell-Segur (AKNS) system for the first time. With the aid of Lax pair of this nonlocal system, Darboux transformation (DT) and new soliton-like solutions are obtained. Different from local equations, Darboux transformation of nonlocal systems needs to meet certain conditions. In this article, under the condition of symmetry reduction, the components of Darboux transformation need to satisfy . In order to study the dynamic information of the solutions, the images of the solutions are given.
Highlights
In the past decades, a number of researches involved in applied mathematics and theoretical physics are concerned with integrable systems
An important research topic is to find the exact solutions of these systems, especially their soliton solutions or soliton-like solutions
The integrable high order nonlocal coupled AKNS system is constructed by using the symmetry reduction method
Summary
A number of researches involved in applied mathematics and theoretical physics are concerned with integrable systems. For system (1.1), the exact solution and the conservation law are studied by the inverse scattering method. PT symmetry; 3) partial reverse space-time symmetry For this new type of system, many scholars have studied the integrability, exact solution [14] [15], conservation law and other aspects of the system, and got a lot of excellent results. The Darboux transform based on Lax pair has been proved to be one of the most effective algorithms for solving explicit solutions of nonlinear evolution equations. By using Darboux transformation method, soliton solutions, rogue-wave solutions of those nonlocal integrable equations are given [20]-[25].
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