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

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.