A solving problem for the Lorenz system in atmospheric physics is considered. First, a set of variational iterations is constructed by using the generalized variation principle. Then, the initial approximate solution is determined. Finally, using the variational iteration, each approximate solution for corresponding model is found. The generalized variational iteration method is an analytic method, and the obtained solution can be analytically operated further.
In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopic mapping method.
Using the homotopic mapping method, a class of nonlinear KdV(Korteweg de Vries) equation is considered. Firstly, by introducing a homotopic transform, the problem of solving soliton for the corresponding equation is changed into a problem of mapping transform. Then on account of the property of the homotopic mapping, the approximate solution of soliton for the original equation is obtained.
A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.
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