Exact Solutions of the Nonlinear Diffusion Equation

[摘要] We construct new radially symmetric exact solutions of the multidimensional nonlinear diffusion equation, which can be expressed in terms of elementary functions, Bessel functions, Jacobi elliptic functions, Lambert W-function, and the exponential integral. We find new self-similar solutions of a spatially one-dimensional parabolic equation similar to the nonlinear heat equation. Our exact solutions can help verify difference schemes and numerical calculations used in the mathematical modeling of processes and phenomena described by these equations.

[学科分类] 数学（综合）

[关键词] multidimensional nonlinear diffusion equation;nonlinear heat equation;self-similar solutions;radially symmetric exact solutions;Abel equation;Jacobi elliptic functions;Lambert W-function