Nonlinear Boussinesq Equation with Beta Effect and Its Multi-soliton Solutions in Barotropic Fluid
The multi-soliton solutions of the governing equations of large scale Rossby waves with beta effect are considered.Firstly,starting from the traditional barotropic quasi-geostrophic potential vorticity equation,the amplitude of large-scale Rossby waves satisfies the nonlinear Bouss-inesq equation with beta effect by using multi-scale analysis,coordinate transformation method,taylor expansion method and separation of variables method.Then,based on this equation,the bilin-ear form of the equation is given through appropriate variable substitution,and 1-soliton solution,2-soliton solution,3-soliton solution and N-soliton solution of the nonlinear Boussinesq equation are obtained by using Hirota bilinear method.Based on the model equation,the generalized beta effect can induce the generation of Rossby waves.And the results show that the amplitude of soliton solu-tion decreases with the increase of nonlinear coefficient.
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