Soliton interactions of a variable-coefficient three-component AB system for the geophysical flows

Abstract

Geophysical flows consist of the large-scale motions of the ocean and/or atmosphere. Researches on the geophysical flows reveal the mechanisms for the transport and redistribution of energy and matter. Investigated in this paper is a variable-coefficient three-component AB system for the baroclinic instability processes in geophysical flows. With respect to the three wave packets as well as the correction to the mean flow, bilinear forms are obtained, and one-, two- and [Formula: see text]-soliton solutions are derived under some coefficient constraints via the Hirota method. Soliton interaction is graphically investigated: (1) Velocities of the [Formula: see text] and [Formula: see text] components and amplitude of the [Formula: see text] component are proportional to the parameter measuring the state of the basic flow, where [Formula: see text] is the [Formula: see text]th wave packet with [Formula: see text] and [Formula: see text] is related to the mean flow; Amplitudes of the [Formula: see text] components decrease with the group velocity increasing; Parabolic-type solitons, sine-type solitons and quasi-periodic-type two solitons are obtained; For the [Formula: see text] component, solitons with the varying amplitudes and dromion-like two solitons are shown; (2) Three types of the breathers with different interaction periods and numbers of the wave branches in a wave packet are analyzed; (3) Bound states are depicted; (4) Compression of the soliton is presented; (5) Interactions between/among the solitons and breathers are also illustrated.