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Exact traveling wave solutions of nonlinear variable-coefficients evolution equations with forced terms using the generalized \((G'/G)\)-expansion method. (English) Zbl 1330.35066

Summary: The exact traveling wave solutions of the nonlinear variable-coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized \((G'/G)\)-expansion method. As a result, hyperbolic, trigonometric, and rational function solutions with parameters are obtained. When these parameters take special values, the solitary wave solutions are derived from the hyperbolic function solution. It is shown that the proposed method is direct, effective and can be applied to many other nonlinear evolution equations in mathematical physics.

MSC:

35C07 Traveling wave solutions
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C08 Soliton solutions
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