Bright solitary waves in a Bose-Einstein condensate and their interactions

TL;DR

This paper investigates the behavior and interactions of bright solitary waves in a Bose-Einstein condensate, highlighting how conservation laws influence their repulsion and merging under specific conditions.

Contribution

It provides new insights into the dynamics of solitary wave interactions, emphasizing the fragile nature of effective repulsion due to conservation laws and symmetry breaking.

Findings

Repulsion occurs in antisymmetric solitary wave combinations due to conservation laws.

Breaking parity and energy relaxation lead to wave merging.

Effective repulsion is fragile and requires nearly ideal conditions.

Abstract

We examine the dynamics of two bright solitary waves with a negative nonlinear term. The observed repulsion between two solitary waves -- when these are in an antisymmetric combination -- is attributed to conservation laws. Slight breaking of parity, in combination with weak relaxation of energy, leads the two solitary waves to merge. The effective repulsion between solitary waves requires certain nearly ideal conditions and is thus fragile.