Symmetries and Integrability of Difference Equations

Autor: Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz

Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore ap

The discretized Boussinesq equation and its conditional symmetry reduction

Autor: Miguel A. Rodriguez, Decio Levi, Zora Thomova

Publikováno v: E-Prints Complutense: Archivo Institucional de la UCM
Universidad Complutense de Madrid
E-Prints Complutense. Archivo Institucional de la UCM
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In this article we show that we can carry out the symmetry preserving discretization of the Boussinesq equation with respect to three of its more significant conditional symmetries. We perform the symmetry reduction of the obtained nonlinear discrete

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd36fd8def9aee2614dda4fe8041a20f

Construction of Partial Differential Equations with Conditional Symmetries

Autor: Miguel A. Rodriguez, Decio Levi, Zora Thomova

Publikováno v: Integrability, Supersymmetry and Coherent States ISBN: 9783030200862

Nonlinear PDEs having given conditional symmetries are constructed. They are obtained starting from the invariants of the conditional symmetry generator and imposing the extra condition given by the characteristic of the symmetry. Series of examples

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28f9493ea671d46c84386d86b49b22aa
https://doi.org/10.1007/978-3-030-20087-9_17

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

Autor: Eugenio Ricca, Zora Thomova, Decio Levi, Pavel Winternitz

The symmetry algebra of the differential-difference equation \documentclass[12pt]minimal\begindocument$\dotu_n = N/D$\enddocumentu?n=N/D with D = un+1 - un?1 and N = P(un)un+1un?1 + Q(un)(un+1 + un?1) + R(un), where P, Q, and R are arbitrary analytic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4a15889d76801fe0efc79d90e641fad1

Contact transformations for difference schemes

Autor: Decio Levi, Christian Scimiterna, Zora Thomova, Pavel Winternitz

""We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28977a35d7f13d3a22f249a132c74375
https://hdl.handle.net/11590/278552