Explicit solitons of Kundu equation derived by Riemann-Hilbert problem

We apply Riemann-Hilbert problem (RHP) to Kundu equation with zero boundary condition. By solving the revised RHP related to N pairs of simple pole points, a pair of differential equations are solved from the asymptotic behaviors, and the explicit formula of N-th order soliton is obtained. Unlike the known representation of N-th order soliton in many literatures, our formula does not include unsatisfactory integral due to using revised RHP. Based on this new formula, the explicit first order soliton is obtained directly, and the explicit second order bound-state soliton (BSS) is also obtained by applying limit technique. Additionally, higher-order soliton and bound-state soliton (BSS) solutions are discussed, and the approximate trajectories of second order BSS solution are studied. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study applies the Riemann-Hilbert problem (RHP) to the Kundu equation with zero boundary condition. By solving the revised RHP, a pair of differential equations are obtained, and the explicit formula for the N-th order soliton is derived. The formula does not involve unsatisfactory integrals, unlike existing representations in literature.