On a class of 2D integrable lattice equations
| Autor: | Evgeny Ferapontov, Ismagil Habibullin, M. N. Kuznetsova, Vladimir Novikov |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematical sciences Integrable system Nonlinear Sciences - Exactly Solvable and Integrable Systems Classification procedure 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics Of the form Conformal map 01 natural sciences Nonlinear Sciences::Exactly Solvable and Integrable Systems Lattice (order) 0103 physical sciences 010307 mathematical physics 0101 mathematics Characteristic variety Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics Mathematics |
| Popis: | We develop a new approach to the classification of integrable equations of the form $$ u_{xy}=f(u, u_x, u_y, \triangle_z u \triangle_{\bar z}u, \triangle_{z\bar z}u), $$ where $\triangle_{ z}$ and $\triangle_{\bar z}$ are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure which is Einstein-Weyl on every solution. (2) Secondly, to the candidate equations selected at the previous step we apply the test of Darboux integrability of reductions obtained by imposing suitable cut-off conditions. |
| Databáze: | OpenAIRE |
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