Localization and shock waves in curved manifolds for the Gross-Pitaevskii equation

TL;DR

This paper studies how geometry and nonlinearity affect Bose-Einstein condensates in curved 3D potentials, revealing topological localization and shock wave phenomena through advanced simulations.

Contribution

It introduces a detailed analysis of the interplay between curvature-induced localization and shock wave formation in nonlinear quantum fluids.

Findings

Topological localization occurs at high curvature.

Curved dispersive shock waves are generated with increased nonlinearity.

Simulations support the interplay between geometry and nonlinear dynamics.

Abstract

We investigate the dynamics of a Bose-Einstein condensate in a progressively bended three dimensional cigar shaped potential. The interplay between geometry and nonlinearity is considered. At high curvature, topological localization occurs and becomes frustrated by the generation of curved dispersive shock-waves when the strength of nonlinearity is increased. The analysis is supported by four-dimensional parallel simulations.