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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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2015-07, Vol.36 (3), p.225-233
Main Authors: Baran, H., Krasil’shchik, I. S., Morozov, O. I., Vojčák, P.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080215030026