Collision Interactions of Solitons in a Baroclinic Atmosphere

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  • 1 Department of Geophysics, Peking University, Beijing, China
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Abstract

In this paper the interactions between two marginally unstable baroclinic wave packets in the two-layer Phillips model are investigated by using the multiple-scale method. It is shown that the interactions can be described by a set of two coupled nonlinear Schrödinger equations. Except for two special cases the equations have only four invariants of motion and cannot be solved by the inverse scattering method.

The equations are solved numerically to study the collision interactions between two solitons. It is found that though the coefficients in the equations are fixed, the behavior of the two solitons may be quite different, which is closely related to the initial states of the two solitons (the speeds and the amplitudes of the solitons well before the interactions). For some initial conditions the collision interactions may be soliton-like in that the properties of the two solitons change very little, while for other initial conditions some “inelastic” phenomena are observed: one soliton may be destroyed by the other, or two solitons may change their speeds and directions of propagation and fuse into a new bound state.

Abstract

In this paper the interactions between two marginally unstable baroclinic wave packets in the two-layer Phillips model are investigated by using the multiple-scale method. It is shown that the interactions can be described by a set of two coupled nonlinear Schrödinger equations. Except for two special cases the equations have only four invariants of motion and cannot be solved by the inverse scattering method.

The equations are solved numerically to study the collision interactions between two solitons. It is found that though the coefficients in the equations are fixed, the behavior of the two solitons may be quite different, which is closely related to the initial states of the two solitons (the speeds and the amplitudes of the solitons well before the interactions). For some initial conditions the collision interactions may be soliton-like in that the properties of the two solitons change very little, while for other initial conditions some “inelastic” phenomena are observed: one soliton may be destroyed by the other, or two solitons may change their speeds and directions of propagation and fuse into a new bound state.

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