New classes of solutions in the Coupled PT Symmetric Nonlocal Nonlinear Schrodinger Equations with Four Wave Mixing

TL;DR

This paper explores new solution types in a nonlocal coupled nonlinear Schrödinger equation with four-wave mixing, revealing how four-wave mixing influences soliton and breather interactions, including the creation of periodic lattices.

Contribution

It introduces a family of exact solutions using Darboux transformation for a generalized nonlocal coupled nonlinear Schrödinger equation with four-wave mixing, highlighting novel solution behaviors.

Findings

Four-wave mixing transforms two-soliton solutions into Akhmediev breathers.

A new spatially and temporally periodic solution called 'Soliton (Breather) lattice' is generated.

Four-wave mixing significantly affects the nature and interactions of solutions.

Abstract

We investigate generalized nonlocal coupled nonlinear Schroedinger equation containing Self-Phase Modulation, Cross-Phase Modulation and Four-Wave Mixing involving nonlocal interaction. By means of Darboux transformation, we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soliton interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of Four-Wave Mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of Four-Wave Mixing results in the generation of a new solution which is spatially and temporally periodic called "Soliton (Breather) lattice".