Collisions between the dark solitons for a nonlinear system in the geophysical fluid

Abstract Under investigation in this paper is a nonlinear system, which can be used to describe the marginally unstable baroclinic wave packets in the geophysical fluid. With the help of this nonlinear system, we study the properties of the dark solitons in the geophysical fluid. With the symbolic computation, dark one- and two-soliton solutions for such a system are obtained. Propagations of the one solitons and collisions between the two solitons are graphically shown and discussed with the parameters α and γ, where α measures the state of the basic flow and γ is the group velocity. γ is observed to affect the amplitudes of the dark one and two solitons, i.e., amplitudes of the solitons become higher with the value of γ increasing, and travelling directions of the two solitons can be influenced by γ. α is observed to affect the plane of B, but have no effect on A, where A represents the amplitude of the wave packet, and B is a quantity measuring the correction of the basic flow.

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