Collisions and fusion of one- and two-dimensional solitons driven by potential troughs in the cubic-quintic nonlinear Schr\"{o}dinger equations

TL;DR

This paper investigates the dynamics of 1D and 2D solitons in the cubic-quintic nonlinear Schrödinger equation with potential troughs, revealing conditions for quasi-elastic and inelastic collisions and symmetry breaking.

Contribution

It introduces a detailed analysis of soliton collisions in a cubic-quintic nonlinear Schrödinger framework with intersecting potential troughs, highlighting new collision behaviors and symmetry-breaking phenomena.

Findings

Gaussian-Gaussian and Gaussian-FT collisions are quasi-elastic.

FT soliton collisions can be inelastic, leading to merger.

Weak radiation is emitted during Gaussian-FT collisions.

Abstract

We study the formation and collision of one- and two-dimensional (1D and 2D) Gaussian-shaped and flat-top (FT) solitons in the framework of the nonlinear Schr\"{o}dinger equation with the cubic-quintic nonlinearity and two intersecting potential troughs. We find that Gaussian-Gaussian and Gaussian-FT collisions between the solitons, steered by the troughs, are quasi-elastic, while the collisions between FT solitons may be either quasi-elastic or inelastic, in the form of merger into a single FT soliton, thus spontaneously breaking the symmetry between the steering troughs. The Gaussian-FT collisions, being overall quasi-elastic, generate weak radiation fields.