Dressing for a novel integrable generalization of the nonlinear Schr\"odinger equation

TL;DR

This paper develops a dressing method for a new integrable extension of the nonlinear Schrödinger equation, deriving explicit N-soliton solutions and simplifying existing formulas for related equations.

Contribution

It introduces a novel integrable generalization of the nonlinear Schrödinger equation and provides explicit soliton solutions, advancing analytical methods in integrable systems.

Findings

Derived explicit formulas for N-soliton solutions

Simplified formulas for derivative nonlinear Schrödinger equation solitons

Enhanced understanding of integrable generalizations

Abstract

We implement the dressing method for a novel integrable generalization of the nonlinear Schr\"odinger equation. As an application, explicit formulas for the $N$-soliton solutions are derived. As a by-product of the analysis, we find a simplification of the formulas for the $N$-solitons of the derivative nonlinear Schr\"odinger equation given by Huang and Chen.