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Riccati function solutions of nonlinear dispersive-dissipative mKdV equations. (Chinese. English summary) Zbl 1212.35405

Summary: The mKdV equation is expanded and a nonlinear dispersive dissipative mKdV equation is obtained as: \(u_t+\alpha u^2u_x+\beta u_{xx}+\gamma u_{xxx}=0\). The generalized modified \(F\)-expansion method is developed to solve nonlinear mathematic physic equations. This method is improved by \(F\)-expansion method in the form of solution and constraint condition. By using the generalized modified \(F\)-expansion method and with the aid of computer symbolism system Mathematica, abundant exact solutions of the nonlinear dispersive dissipative mKdV equation are obtained, including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, exponential solutions, periodic wave solutions, solitary wave solutions, triangle function solutions, rational function solutions, and plural number formal solutions, etc..

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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