## The extended Riccati equation mapping method for variable-coefficient diffusion-reaction and mKdV equations.(English)Zbl 1210.35210

Summary: The extended Riccati equation mapping method is proposed to seek exact solutions of variable-coefficient nonlinear evolution equations. Being concise and straightforward, this method is applied to certain type of variable-coefficient diffusion-reaction equation and variable-coefficient mKdV equation. By means of this method, hyperbolic function solutions and trigonometric function solutions are obtained with the aid of symbolic computation. It is shown that the proposed method is effective, direct and can be used for many other variable-coefficient nonlinear evolution equations.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 35C09 Trigonometric solutions to PDEs 35A24 Methods of ordinary differential equations applied to PDEs

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### References:

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