含时系数Gardner方程的增强群分类
Enhanced group classification of Gardner equations with time-dependent coefficients
摘要：
本文对变系数Gardner方程（又称组合KdV-mKdV方程）的Lie对称性进行了分类。与Molati和Ramollo（2012）中提出的特定结果相反，我们执行穷举组分类。结果表明，利用等价变换对类的任意元素进行规范或类间映射的方法都可以得到完整的结果。作为第二种方法的副产品，我们得到了一类带强迫项的变系数mKdV方程的完全群分类。与通常的相比，使用广义扩展等价群的优点也进行了讨论。
英文摘要：
We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdV-mKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive group classification. It is shown that the complete result can be achieved using either the gauging of arbitrary elements of class by the equivalence transformations or the method of mapping between classes. As by-product of the second approach the complete group classification of a class of variable coefficient mKdV equations with forcing term is derived. Advantages of the use of the generalized extended equivalence group in comparison with the usual one are also discussed.
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