Systematic solitary waves by linear limit continuation from two anisotropic traps in two-dimensional Bose-Einstein condensates

TL;DR

This paper applies linear limit continuation to systematically construct and analyze solitary waves in two-dimensional Bose-Einstein condensates under anisotropic traps, revealing various wave patterns and their connectivity.

Contribution

It demonstrates the effectiveness of linear limit continuation in finding and connecting solitary wave solutions in anisotropic traps for Bose-Einstein condensates.

Findings

Identified multiple wave patterns in near-linear regimes.

Successfully continued solutions into the Thomas-Fermi and isotropic regimes.

Discussed the parametric connectivity of solitary waves.

Abstract

Linear limit continuation was recently developed as a systematic and effective method for constructing numerically exact solitary waves from their respective linear limits. In this work, we apply the technique to two typical anisotropic harmonic traps in two-dimensional Bose-Einstein condensates to further establish the method and also to find more solitary waves. Many wave patterns are identified in the near-linear regime and they are subsequently continued into the Thomas-Fermi regime, and then they are further continued into the isotropic trap if possible. Finally, the parametric connectivity of the pertinent solitary waves is also discussed.