Exact solutions of the reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation

TL;DR

This paper explores a reverse space-time higher-order modified self-steepening nonlinear Schrödinger equation, demonstrating its integrability and constructing diverse localized wave solutions with novel behaviors using Darboux transformation.

Contribution

It introduces the first systematic construction of solutions for a nonlocal reverse space-time nonlinear Schrödinger equation, revealing unique wave dynamics.

Findings

Verified integrability via Lax pair and conservation laws

Constructed diverse localized wave solutions including rogue waves and solitons

Identified novel dynamical behaviors not present in local equations

Abstract

This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this nonlocal equation is rigorously verified by presenting its associated Lax pair and infinitely many conservation laws. Utilizing the Darboux transformation, we systematically construct a diverse range of localized wave solutions on both zero and nonzero backgrounds. These patterns, such as kinks, exponentially decaying solitons, asymmetric rogue waves and their interaction solutions, exhibit novel dynamical behaviors that are not found in the local counterparts. This work not only enriches the family of solutions for the equation, but also highlights the effectiveness of the Darboux transformation in exploring nonlinear wave dynamics in nonlocal systems.