标题： (2+1)维非线性扩散方程的等价群和微分不变量 显示英文标题

标题： Equivalence Groups and Differential Invariants for (2+1) dimensional Nonlinear Diffusion Equation

摘要： (2+1)维扩散方程在等价变换的框架下被考虑。 群的生成元被获得，并检查了线性与非线性方程之间的可接受变换。 结果表明，当独立变量的生成元依赖于因变量时，线性与非线性方程之间的变换是可能的。 获得了一些非线性方程的精确解。 研究了与变换群相关的微分不变量，并将结果与直接积分方法进行了比较。 显示英文摘要

摘要： (2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown that transformations between linear and nonlinear equations are possible provided that the generators of independent variables depend on the dependent variable. Exact solutions for some nonlinear equations are obtained. Differential invariants related to the transformation groups are investigated and the results are compared with the direct integration method.