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RLW-Burgers方程的势对称及其精确解Potential Symmetry and Exact Solutions of RLW-Burgers Equation
鲍春玲, 苏道毕力格, 韩雁清
势对称, 微分特征列集算法, 推广的Tanh函数法, RLW-Burgers方程, 精确解Potential Symmetry, Differential Characteristic Set Algorithm, Extended Tanh Function Method, RLW-Burgers Equation, Exact Solutions
《Advances in Applied Mathematics》, Vol.5 No.1, 2016-02-26
We expanded the classical symmetries of RLW-Burgers equation by calculating the potential symmetries, and we obtained a series of new exact solutions of RLW-Burgers equation. Firstly, we determined the classical symmetries and potential symmetries of RLW-Burgers equation based on differential characteristic set algorithm. Secondly, we constructed the invariant solutions of Burgers equation by using the extended Tanh function method, and these solutions with arbitrary pa-rameters are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, respectively. Finally, new exact solutions for RLW-Burgers equation are obtained by acting Lie transformation group of potential symmetry and the classical symmetry on the invariant solutions. It is important that these solutions can not be obtained from classical symmetries of Burgers equation.