Baseband modulational instability and dynamics of rogue waves in coherently coupled Bose–Einstein condensates

Abstract

We consider coupled dimensionless Gross-Pitaevskii (GP) equations that describes effective coherently coupled Bose–Einstein condensates (BECs) trapped in external complex potentials. Through a modified similarity transformation, the integrability condition is obtained and the system is reduced to one single integrable autonomous cubic-quintic nonlinear Schrödinger (NLS) equation with self-steepening and self-frequency shift. The baseband modulational instability (MI) for the obtained NLS equation is investigated in details. Through the exact first- and second-order rogue wave solutions with nonlinear chirp of the coupled GP equation, we investigate analytically the propagation dynamics of rogue waves on weakly perturbed continuous wave solutions in the parameter space where the baseband MI exist. Our results show that one can manipulate the motion of matter rogue waves by controlling the external trapping potential. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband MI occurs. Our results show how multiplet first- and second-order rogue waves can be generated by varying some solution parameters such as the amplitude parameter.