Superposed nonlinear waves in coherently coupled Bose-Einstein condensates

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 Schrödinger 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.

13 figures

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Instabilities, breathers and rogue waves in optics
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Faraday waves in binary non-miscible Bose-Einstein condensates
• Multicomponent coherently coupled and incoherently coupled solitons and their collisions
• Stabilization of a Bose-Einstein droplet by hyperfine Rabi oscillations
• Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings
• Matter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates
• Scattering of matter-waves in spatially inhomogeneous environments
• Interactions and Collisions of Discrete Breathers in Two-Species Bose-Einstein Condensates in Optical Lattices