Superposed nonlinear waves in coherently coupled Bose–Einstein condensates

• Coherently coupled Gross–Pitaevskii equations with constant and time-dependent nonlinearities are considered.
• Novel superposed nonlinear structures are reported.
• Breather collision and nontrivial twin-peak rogue wave are explored.
• Co-existing breathers and rogue waves are observed.
• Creeping solitons and compression mechanism, respectively for periodically modulated and kink-like nonlinearity are identified.

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 coefficients. 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.