Darboux transformation and exact solution to the nonlocal Kundu-Eckhaus equation

In this paper, the n-component nonlocal Kundu-Eckhaus equation is presented. The Darboux transformation to the nonlocal Kundu-Eckhaus equation is con-structed to obtain the N-soliton solution to the equation. The difference between the solution obtained here and that of the local Kundu-Eckhaus equation by Darboux transformation is that the solution of the former has symmetric con-straints. Besides, the one-exact solution to the nonlocal Kundu-Eckhaus equation is obtained. For example, as for the three-component nonlocal KE equation, the images of the corresponding rogue wave solutions are drawn by taking specific parameters.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, the n-component nonlocal Kundu-Eckhaus equation and its Darboux transformation are presented. The N-soliton solution and the one-exact solution to the equation are obtained. The difference between the solutions of the nonlocal and local Kundu-Eckhaus equations is that the former has symmetric constraints. Furthermore, specific parameters are used to draw the images of rogue wave solutions for a three-component nonlocal KE equation.