2003/08/31 by O. V. Kaptsov, О. В. Капцов, Kaptsov, O. V. +2
Mathematics · Physics and Astronomy · #34G20 #35K57 #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:34G20 #msc:35K57
paper · pdf · doi:10.48550/arxiv.math-ph/0309001
30 pages, TeX
arxiv created 2003/08/31 · openalex publication_date 2003/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach non-linear heat equations and Gibbons-Tsarev's equation are discussed. We introduce the notion of an invariant solution under an involutive distribution and give sufficient conditions for existence of such a solution.