Integrability and rational soliton solutions for gauge invariant derivative nonlinear Schrödinger equations

Abstract

The present work addresses the study and characterization of the integrability of three famous nonlinear Schrödinger equations with derivative-type nonlinearities in 1+1 dimensions. Lax pairs for these three equations are successfully obtained by means of a Miura transformation and the singular manifold method. After implementing the associated binary Darboux transformations, we are able to construct rational soliton-like solutions for those systems.

5 pages, 2 figures. Based on the contribution presented at the "Third BYMAT Conference: Bringing Young Mathematicians Together", December 1--3, 2020, Valencia, Spain. To appear in the Proceedings of the Third BYMAT Conference