2023/05/19 by Kaptsov Oleg, Oleg, Kaptsov
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Boundary Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2305.11422
openalex publication_date 2023/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider mappings of jet spaces that preserve the module of canonical Pfaffian forms, but are not generally invertible. These mappings are called contact. A lemma on the prolongation of contact mappings is proved. Conditions are found for which mappings transform solutions of some partial differential equations into ones of other equations. Examples of contact mappings of differential equations are given. We consider contact mappings depending on a parameter and give example of differential equation invariant under the maps.