Simple waves in a two-component Bose-Einstein condensate

TL;DR

This paper analyzes simple wave dynamics in a two-component Bose-Einstein condensate using reduced differential equations, providing analytic solutions for different interaction regimes and confirming results with numerical simulations.

Contribution

It introduces a reduction of the Gross-Pitaevskii equations to Ovsyannikov's system for simple waves and solves it analytically for various interaction differences.

Findings

Analytic solutions for simple wave evolution in two-component BECs.

Confirmation of analytic results through numerical simulations.

Insights into wave behavior under different inter- and intra-species interactions.

Abstract

We consider dynamics of simple waves in a two-component Bose-Einstein condensates. The evolution of the condensate is described by the Gross-Pitaevskii equations which can be reduced for simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fuid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between inter-species and intra-species nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.