Classification of semidiscrete hyperbolic type equations. The case of third order symmetries
| Autor: | Garifullin, R. N. |
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| Jazyk: | ruština |
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here is the unknown function $u_n (x)$ depends on one discrete $n$ and one continuous $x$ variables. The classification is based on the requirement for the existence of higher symmetries in the discrete and continuous directions. The case is considered when the symmetries are of order 3 in both directions. As a result, a list of equations with the required conditions is obtained. Comment: 15 pages (in Russian) |
| Databáze: | arXiv |
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