Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries
| Autor: | Garifullin, R. N. |
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| Jazyk: | ruština |
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The work deals with the qualification of semidiscrete hyperbolic type equations. We study a class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here the unknown function $u_n(x)$ depends on one discrete $n$ and one continuous $x$ variables. Qualification is based on the requirement of the existence of higher symmetries. The case is considered when the symmetry is of order 5 in continuous directions. As a result, a list of four equations with the required conditions is obtained. For one of the found equations, a Lax representation is constructed. Comment: 11 pages (in Russian) |
| Databáze: | arXiv |
| Externí odkaz: |
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