Abstract
This paper presents a study of the traditional approximation potential vorticity equation. A nonlinear forced Zakharov-Kuznetsov equation by using the perturbation expansion method and multiple temporal and spatial scales method is obtained. And the multiple kink solutions of the forced Zakharov-Kuznetsov equation are obtained and the one- and two-soliton solutions are given by making use of the simplest equation method, namely the coupled Burgers’ equation, which is of a low-order than obtained equation and the multiple kink solutions of the equation are already given by utilizing the simplified Hirota's method. The results show that the proposed method is a powerful mathematical method to solve the nonlinear evolution equation arising in various areas of nonlinear science. Based on the one- and two-soliton solutions, graphical figures are portrayed by taking definite values to parameters and the features of the variable parameters are discussed in detail. Some results are given about interaction of two-soliton solutions and we found the wave amplitude of the two-soliton is influenced with the Coriolis parameters. Meanwhile, the soliton of the model with the external source is also obtained.
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