Nonlinear functional substitutions method for nonlinear diffusion and wave equations

Title	Nonlinear functional substitutions method for nonlinear diffusion and wave equations
Authors	V. M. Morozov^{1, 2}, V. M. Zhuravlev³ ¹Samara National Research University ²Ulyanovsk instrument manufacturing design bureau ³Ulyanovsk State University
Annotation	In 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.
Keywords	functional substitutions method, Backlund transformation, nonlinear diffusion
Citation	Morozov 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: 19.05.2024.