论文标题
（1+2） - 维反应扩散方程的类别的完整谎言对称分类
A complete Lie symmetry classification of a class of (1+2)-dimensional reaction-diffusion-convection equations
论文作者
论文摘要
在时间和两个空间变量的情况下，正在研究一类描述物理，生物学，化学等各种过程的非线性反应 - 扩散方程。构建了等效转换组，用于通过众所周知的算法来得出此类方程类别的谎言对称分类。 事实证明，该算法导致32个反应 - 扩散反射方程，承认非平凡的谎言对称性。此外，为了减少这一数量的方程并获得完整的谎言对称分类，还构建了该类别的一组形式性的变换。结果，所谓的所有不相等方程式的所谓规范列表允许非平凡的谎言对称性（直至任何点转换）及其谎言对称性。该列表由22个方程组成，结果表明，任何其他反应 - 扩散 - 转移方程承认非平凡的谎言对称性都是可以减少这22个方程之一。作为一个非平凡的示例，在带有汉堡项的多孔 - 法式类型方程中，将得出的对称性应用于还原并找到精确的解决方案。
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is constructed, which is applied for deriving a Lie symmetry classification for the class of such equations by the well-known algorithm. It is proved that the algorithm leads to 32 reaction-diffusion-convection equations admitting nontrivial Lie symmetries. Furthermore a set of form-preserving transformations for this class is constructed in order to reduce this number of the equations and obtain a complete Lie symmetry classification. As a result, the so called canonical list of all inequivalent equations admitting nontrivial Lie symmetry (up to any point transformations) and their Lie symmetries are derived. The list consists of 22 equations and it is shown that any other reaction-diffusion-convection equation admitting a nontrivial Lie symmetry is reducible to one of these 22 equations. As a nontrivial example, the symmetries derived are applied for the reduction and finding exact solutions in the case of the porous-Fisher type equation with the Burgers term.
