Solitons and solitonic vortices in a strip

TL;DR

This paper investigates the ground states of matter wave solitons in a strip geometry, showing a transition from one-dimensional solitons to solitonic vortices as the strip width increases, with explicit phase behavior analysis.

Contribution

It provides a rigorous analysis of the ground state transitions in a strip for the Gross-Pitaevskii energy, including explicit phase expressions for large widths.

Findings

Ground state is a 1D soliton for small widths.

Ground state becomes a solitonic vortex for large widths.

Explicit phase decay behavior is characterized.

Abstract

We study the ground state of the Gross Pitaveskii energy in a strip, with a phase imprinting condition, motivated by recent experiments on matter waves solitons. We prove that when the width of the strip is small, the ground state is a one dimensional soliton. On the other hand, when the width is large, the ground state is a solitonic vortex. We provide an explicit expression for the limiting phase of the solitonic vortex as the size of the strip is large: it has the same behaviour as the soliton in the infinite direction and decays exponentially due to the geometry of the strip, instead of algebraically as vortices in the whole space.