Superposed nonlinear waves in coherently coupled Bose-Einstein condensates

TL;DR

This paper explores the dynamics of superposed nonlinear waves in coherently coupled Bose-Einstein condensates, revealing complex structures like rogue waves, breathers, and solitons through transformations of coupled Gross-Pitaevskii equations.

Contribution

It introduces a method to transform coupled Gross-Pitaevskii equations into scalar equations, enabling the analysis of diverse nonlinear wave structures in both autonomous and non-autonomous systems.

Findings

Superposition leads to rogue wave-Ma breather coexistence.

Identification of Akhmediev-Ma breather interactions.

Observation of soliton compression and creeping solitons.

Abstract

We study the dynamics of superposed nonlinear waves in coherently coupled Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity co-efficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schr\"odinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev-Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient.