Dynamics of nonlinear-Schroedinger breathers in a potential trap

TL;DR

This paper investigates the behavior of nonlinear Schroedinger breathers in a potential trap, revealing how gravity influences their splitting and formation of co-hopping or pseudo-breather states, with both analytical and numerical insights.

Contribution

It provides new analytical and numerical analysis of breather dynamics under gravity in a potential trap, applicable to Bose-Einstein condensates and nonlinear optics.

Findings

Breather splits into fundamental solitons near the floor without gravity.

Gravity causes breathers to always split into co-hopping solitons.

Analytical expressions describe the splitting and co-hopping phenomena.

Abstract

We consider the evolution of the 2-soliton (breather) of the nonlinear Schroedinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard floor. This setting can be implemented in atomic Bose-Einstein condensates, and in a nonlinear planar waveguide in optics. In the absence of the gravity, repulsion of the breather from the floor leads to its splitting into constituent fundamental solitons, if the initial distance from the floor is smaller than a critical value; otherwise, the moving breather persists. In the presence of the gravity, the breather always splits into a pair of "co-hopping" fundamental solitons, which may be frequency-locked in the form of a quasi-breather, or unlocked, forming an incoherent pseudo-breather. Some essential results are obtained in an analytical form, in addition to the systematic numerical investigation.