The explicit bound-state soliton of Kundu equation derived by Riemann-Hilbert problem

With zero boundary condition, a revised Riemann-Hilbert problem (RHP) for Kundu equation is provided. Assuming the refection coefficient having one pair of Nth order poles, the RHP is solved, the expression of integral factor involved in the solution is also solved, and the explicit formula of Nth order bound-state soliton of Kundu equation is presented. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper provides a revised Riemann-Hilbert problem for the Kundu equation with zero boundary condition. By assuming the reflection coefficient having one pair of Nth order poles, the RHP is solved and the expression of the integral factor involved in the solution is obtained. An explicit formula for the Nth order bound-state soliton of the Kundu equation is also presented.