Differential constraints and exact solutions of nonlinear diffusion equations

2002/04/17 by О. В. Капцов, Oleg V. Kaptsov, Igor V. Verevkin +1
Mathematics · Physics and Astronomy · #Applied mathematics #Differential equation #Diffusion #Homogeneous space #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Numerical methods for differential equations #Numerical partial differential equations #Physics #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/36/5/315

arxiv created 2002/04/17 · openalex publication_date 2003/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries.

Citations

• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• The construction of special solutions to partial differential equations