•  

Nonlinear functional substitutions method for nonlinear diffusion and wave equations

TitleNonlinear functional substitutions method for nonlinear diffusion and wave equations
AuthorsV. M. Morozov1, 2, V. M. Zhuravlev3
1Samara National Research University
2Ulyanovsk instrument manufacturing design bureau
3Ulyanovsk State University
AnnotationIn this work we develop a generalization of the functional substitutions method --- nonlinear functional substitutions (NFS), based on a nonlinear system of basic relations. Using NFS, Backlund transformations and exact solutions of the Liouville and diffusion equations are constructed.
Keywordsfunctional substitutions method, Backlund transformation, nonlinear diffusion
CitationMorozov V. M., Zhuravlev V. M. ''Nonlinear functional substitutions method for nonlinear diffusion and wave equations'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 166-170. Available at: https://conf.svmo.ru/files/2023/papers/paper26.pdf. - Date of access: 22.06.2024.