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Five-dimensional lax-integrable equation, its reductions and recursion operator
We consider a five-dimensional nonlinear PDE associated to the five-dimensional equation introduced byMartínez Alonso and Shabat. For our equation we find differential coverings with non-removable parameters and list its reductions to known 4D and 3D integrable equations. One of the coverings produc...
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Published in: | Lobachevskii journal of mathematics 2015-07, Vol.36 (3), p.225-233 |
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container_issue | 3 |
container_start_page | 225 |
container_title | Lobachevskii journal of mathematics |
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creator | Baran, H. Krasil’shchik, I. S. Morozov, O. I. Vojčák, P. |
description | We consider a five-dimensional nonlinear PDE associated to the five-dimensional equation introduced byMartínez Alonso and Shabat. For our equation we find differential coverings with non-removable parameters and list its reductions to known 4D and 3D integrable equations. One of the coverings produces a new family of integrable 5D equations. We show that each pair of these equations is related by a Bäcklund transformation, including the Bäcklund auto-transformation for each equation from the family. Also we find a recursion operator for symmetries of the equation and study its action. |
doi_str_mv | 10.1134/S1995080215030026 |
format | article |
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For our equation we find differential coverings with non-removable parameters and list its reductions to known 4D and 3D integrable equations. One of the coverings produces a new family of integrable 5D equations. We show that each pair of these equations is related by a Bäcklund transformation, including the Bäcklund auto-transformation for each equation from the family. Also we find a recursion operator for symmetries of the equation and study its action.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080215030026</doi><tpages>9</tpages></addata></record> |
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subjects | Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes |
title | Five-dimensional lax-integrable equation, its reductions and recursion operator |
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