Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schr\"{o}dinger equation

TL;DR

This paper investigates how small quintic nonlinearities and resonant nonlinearity management influence the stability and splitting of second-order solitons in the nonlinear Schrödinger equation, with applications to optics and Bose-Einstein condensates.

Contribution

It demonstrates that weak quintic nonlinearity can stabilize or destabilize second-order solitons and broadens their resonant response to nonlinearity management.

Findings

Self-focusing quintic term stabilizes 2-solitons.

Self-defocusing quintic term accelerates soliton splitting.

Resonant response broadens with quintic nonlinearity sign.

Abstract

We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain, and to BEC, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one-dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic nonlinearity accelerates its splitting. It is also shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader, in terms of the frequency.