Stability of the solutions of the Gross-Pitaevskii equation

TL;DR

This paper investigates the stability properties of solutions to the Gross-Pitaevskii equation, revealing how static and dynamic stability are interconnected and providing insights into their relationship.

Contribution

It systematically analyzes the connection between static and dynamic stability of solutions to the Gross-Pitaevskii equation, clarifying conditions under which each type of stability occurs.

Findings

Static stability always implies dynamic stability.

Dynamic stability can exist even when static stability is absent.

Static properties reflect features of dynamic stability.

Abstract

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.