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Sophocleous, C. and Wiltshire, R.J. (2006) Linearisation and Potential Symmetries of Certain Systems of Diffusion Equations. Physica A, 370, 329-345. http://dx.doi.org/10.1016/j.physa.2006.03.003

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期刊名称: 《Advances in Applied Mathematics》, Vol.5 No.1, 2016-02-26

摘要: 通过计算RLW-Burgers方程的势对称扩大了其古典对称，并获得了RLW-Burgers方程的一系列新的精确解。首先，基于微分特征列集算法确定了RLW-Burgers方程的古典对称和势对称。其次，利用推广的Tanh函数法构造了RLW-Burgers方程的不变解，这些解分别以含任意参数的双曲函数、三角函数和有理函数表示。最后，分别选择一个势对称和古典对称的Lie变换群，将其作用于RLW-Burgers方程的不变解上获得了新的精确解，重要的是这些解都不能由方程的古典对称得到。 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.