Non-Point Invertible Transformations and Integrability of Partial Difference Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Non-Point Invertible Transformations and Integrability of Partial Difference Equations
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| Creator |
Startsev, S.Y.
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| Description |
This article is devoted to the partial difference quad-graph equations that can be represented in the form φ(u(i+1,j),u(i+1,j+1))=ψ(u(i,j),u(i,j+1)), where the map (w,z)→(φ(w,z),ψ(w,z)) is injective. The transformation v(i,j)=φ(u(i,j),u(i,j+1)) relates any of such equations to a quad-graph equation. It is proved that this transformation maps Darboux integrable equations of the above form into Darboux integrable equations again and decreases the orders of the transformed integrals by one in the j-direction. As an application of this fact, the Darboux integrable equations possessing integrals of the second order in the j-direction are described under an additional assumption. The transformation also maps symmetries of the original equations into symmetries of the transformed equations (i.e. preserves the integrability in the sense of the symmetry approach) and acts as a difference substitution for symmetries of a special form. The latter fact allows us to derive necessary conditions of Darboux integrability for the equations defined in the first sentence of the abstract.
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| Date |
2019-02-10T10:33:27Z
2019-02-10T10:33:27Z 2014 |
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| Type |
Article
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| Identifier |
Название / S.Y. Startsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 18 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 39A14; 37K05; 37K10; 37K35 DOI:10.3842/SIGMA.2014.066 http://dspace.nbuv.gov.ua/handle/123456789/146625 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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