Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

TL;DR

This paper applies the averaging method to Bose-Einstein condensates to analyze the existence, stability, and instability of modulated amplitude waves with nonzero phases, addressing complex singularities.

Contribution

It introduces a framework for analyzing modulated amplitude waves with nontrivial phases in BECs using averaging, extending previous work to more complex phase structures.

Findings

Location of modulated amplitude waves determined

Stability and instability conditions identified

Addresses singularities due to nonzero phases

Abstract

In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and we also study the stability and instability of modulated amplitude waves (periodic or quasi-periodic). Compared with the previous work, modulated amplitude waves studied in this paper have nontrivial phases and this makes the problem become more diffcult, since it involves some singularities.