Nonlinear waves of polarization in two-component Bose-Einstein condensates

TL;DR

This paper explores nonlinear wave phenomena in two-component Bose-Einstein condensates, revealing new soliton behaviors described by the Gardner equation under certain interaction conditions.

Contribution

It demonstrates that the second mode of polarization waves can be modeled by the Gardner equation, expanding the understanding of nonlinear excitations in BECs beyond the KdV framework.

Findings

Second mode described by Gardner equation under specific conditions

Rich variety of nonlinear excitations identified

Different sound velocities for in-phase and counter-phase modes

Abstract

Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.