Zhou Xianchun

The extended auxiliary equation method for the KdV equation with variable coefficients

This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.

Homotopic mapping solitary traveling wave solutions for the disturbed BKK mechanism physical model

Using the trial equation method, a Broer—Kau—Kupershmidt (BKK) mechanism physical model is obtained, and the exact and approximate solitary traveling wave solutions are found. As an example, it is pointed out that the solitary traveling wave approximate solutions have better accurate degree by using the homotopic mapping theory.

A method of solving a class of disturbed Lorenz system

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.