A General Integrable Nonlocal Coupled Nonlinear Schr\"odinger Equation

TL;DR

This paper introduces a new integrable nonlocal coupled nonlinear Schrödinger system with PT symmetry, deriving its soliton solutions via Darboux transformation, expanding the understanding of nonlocal integrable models.

Contribution

It develops a general integrable nonlocal coupled NLS system with PT symmetry and constructs its Nth Darboux transformation for soliton solutions.

Findings

Derived the general nonlocal coupled NLS system with PT symmetry.

Constructed the Nth Darboux transformation for the system.

Obtained explicit soliton solutions using the Darboux transformation.

Abstract

In this paper, we investigate a general integrable nonlocal coupled nonlinear schr\"odinger (NLS) system with the the parity-time (PT) symmetry, which contains not only the nonlocal self-phase modulation and the nonlocal cross-phase modulation, but also the nonlocal four-wave mixing terms. This nonlocal coupled NLS system is a nonlocal version of a coupled NLS system. The general Nth Darboux transformation for the nonlocal coupled NLS equation is constructed. By using the Darboux transformation, its soliton solutions are obtained.