Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation

TL;DR

This paper analyzes the stability and bifurcation properties of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation, revealing new decay mechanisms and bistability phenomena.

Contribution

It provides a comprehensive characterization of soliton solutions, bistability, and instabilities using catastrophe theory in the cubic-quintic nonlinear Schrödinger framework.

Findings

Identification of bistability regions for dark-antidark solitons

Discovery of new decay mechanisms for antidark solitons

Full characterization of soliton existence and stability regimes

Abstract

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.