Integrability of two-component nonautonomous nonlinear Schr\"odinger equation

TL;DR

This paper explores the conditions under which nonautonomous two-component nonlinear Schrödinger equations, modeling Bose-Einstein condensates, are integrable, revealing the physical balance necessary for nonautonomous soliton existence and dynamics.

Contribution

It provides new integrability conditions for generalized nonautonomous NLS equations in multi-component BECs, clarifying the physical origin of nonautonomous solitons and their controllable dynamics.

Findings

Integrability depends on the balance between dispersion, external potential, and nonlinearity.

All combinations of intra- and inter-component interactions can support nonautonomous solitons.

Controlling experimental parameters influences the dynamics of two-component BECs.

Abstract

We investigate the integrability of generalized nonautonomous nonlinear Schr\"odinger (NLS) equations governing the dynamics of the single- and double-component Bose-Einstein condensates (BECs). The integrability conditions obtained indicate that the existence of the nonautonomous soliton is due to the balance between the different competition features: the kinetic energy (dispersion) versus the harmonic external potential applied and the dispersion versus the nonlinearity. In the double-component case, it includes all possible different combinations between the dispersion and nonlinearity involving intra- and inter-interactions. This result shows that the nonautonomous soliton has the same physical origin as the canonical one, which clarifies the nature of the nonautonomous soliton. Finally, we also discuss the dynamics of two-component BEC by controlling the relevant experimental parameters.