Triple-pole soliton solutions of the derivative nonlinear Schrodinger equation via inverse scattering transform

We construct the triple-pole soliton solutions to the classical DNLS (derivative nonlinear Schrodinger) equation with zero boundary conditions at infinity through the inverse scattering transform method. Under the condition that the scattering coefficient has N-triple zeros, the detailed analysis of the discrete spectrum in direct problem is presented. The inverse problem is formulated and solved by means of the matrix Riemann-Hilbert problem with triple poles. As a consequence, we obtain the general solution of the DNLS equation. Moreover, the explicit N-triple-poles soliton formula for the reflectionless potential is derived. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The triple-pole soliton solutions to the classical DNLS equation with zero boundary conditions at infinity are constructed using the inverse scattering transform method. Detailed analysis of the discrete spectrum in the direct problem is presented under the condition of the scattering coefficient having N-triple zeros. The general solution of the DNLS equation and an explicit N-triple-poles soliton formula for the reflectionless potential are obtained through the matrix Riemann-Hilbert problem with triple poles.