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On a class of 2D integrable lattice equations
We develop a new approach to the classification of integrable equations of the form uxy = f(u, ux, uy, Δzu Δz¯u, Δ zz¯u) where Δz and Δz¯ are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of t...
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| Main Authors: | , , , |
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| Format: | Default Article |
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2020
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| Online Access: | https://hdl.handle.net/2134/12559481.v1 |
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| _version_ | 1818167452436004864 |
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| author | Evgeny Ferapontov Ismagil Habibullin Mariya Kuznetsova Vladimir Novikov |
| author_facet | Evgeny Ferapontov Ismagil Habibullin Mariya Kuznetsova Vladimir Novikov |
| author_sort | Evgeny Ferapontov (1259199) |
| collection | Figshare |
| description | We develop a new approach to the classification of integrable equations of the form uxy = f(u, ux, uy, Δzu Δz¯u, Δ zz¯u) where Δz and Δz¯ 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 |
| format | Default Article |
| id | rr-article-12559481 |
| institution | Loughborough University |
| publishDate | 2020 |
| record_format | Figshare |
| spelling | rr-article-125594812020-07-13T00:00:00Z On a class of 2D integrable lattice equations Evgeny Ferapontov (1259199) Ismagil Habibullin (9023975) Mariya Kuznetsova (9023978) Vladimir Novikov (1259079) Mathematical Physics Mathematical Sciences Physical Sciences Darboux integrability. dispersionless Lax pair Einstein-Weyl geometry characteristic variety 2D lattice equations We develop a new approach to the classification of integrable equations of the form u<sub>xy</sub> = f(u, u<sub>x</sub>, u<sub>y</sub>, Δ<sub>z</sub>u Δ<sub>z¯</sub>u, Δ <sub>zz¯</sub>u) where Δ<sub>z </sub> and Δ<sub>z</sub><sub>¯ </sub>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 2020-07-13T00:00:00Z Text Journal contribution 2134/12559481.v1 https://figshare.com/articles/journal_contribution/On_a_class_of_2D_integrable_lattice_equations/12559481 All Rights Reserved |
| spellingShingle | Mathematical Physics Mathematical Sciences Physical Sciences Darboux integrability. dispersionless Lax pair Einstein-Weyl geometry characteristic variety 2D lattice equations Evgeny Ferapontov Ismagil Habibullin Mariya Kuznetsova Vladimir Novikov On a class of 2D integrable lattice equations |
| title | On a class of 2D integrable lattice equations |
| title_full | On a class of 2D integrable lattice equations |
| title_fullStr | On a class of 2D integrable lattice equations |
| title_full_unstemmed | On a class of 2D integrable lattice equations |
| title_short | On a class of 2D integrable lattice equations |
| title_sort | on a class of 2d integrable lattice equations |
| topic | Mathematical Physics Mathematical Sciences Physical Sciences Darboux integrability. dispersionless Lax pair Einstein-Weyl geometry characteristic variety 2D lattice equations |
| url | https://hdl.handle.net/2134/12559481.v1 |