Vector bright soliton interactions of the two-component AB system in a baroclinic fluid

Abstract

A two-component AB system, which describes the wave-packets in a baroclinic fluid, is investigated in this paper. Bright one- and two-soliton solutions are constructed via the Hirota method. We derive the degenerate and nondegenerate vector solitons associated with the one and two wave numbers, respectively, and the latter admit both the single- and double-hump profiles. Effects of the supercritical / subcritical coefficient μ and nonlinearity coefficient σ in that system on the wave packets A 1 and A 2 are analysed: Velocities of A 1 , A 2 and the wave-induced modification of the basic flow, B , are proportional to μ , amplitudes of A 1 and A 2 are inversely proportional to σ , and amplitude of B is proportional to μ . Via the asymptotic analysis, we find that (1) the interactions between the two degenerate solitons or two nondegenerate solitons can be elastic under certain conditions, otherwise the interactions are shape-changing with the total energy in each soliton (consisting of all the components) being conserved; (2) the interactions between the nondegenerate and degenerate solitons are shape-changing, and the nondegenerate solitons can remain the double-hump shape or change to the periodic oscillation after the interactions; (3) the energy redistribution between the A 1 and A 2 components occurs when the two degenerate solitons undergo the shape-changing interaction, and the nondegenerate soliton undergoes the interaction without any intensity redistribution.