Integrability properties of some equations obtained by symmetry reductions

DOI

10.1080/14029251.2015.1023582How to use a DOI?

Keywords

Partial differential equations; symmetry reductions; solutions; the Gibbons-Tsarev equation; Lax-integrable equations

Abstract

In our recent paper [1], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non-removable parameter) 3-dimensional equations. Here we study the behavior of the integrability features of the initial equations under the reduction procedure. We show that the ZCRs are transformed to nonlinear differential coverings of the resulting 2D-systems similar to the one found for the Gibbons-Tsarev equation in [17]. Using these coverings we construct infinite series of (nonlocal) conservation laws and prove their nontriviality. We also show that the recursion operators are not preserved under reductions.

Copyright

© 2015 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - H. Baran
AU  - I.S. Krasil′shchik
AU  - O.I. Morozov
AU  - P. Vojčák
PY  - 2021
DA  - 2021/01/06
TI  - Integrability properties of some equations obtained by symmetry reductions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 210
EP  - 232
VL  - 22
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.1023582
DO  - 10.1080/14029251.2015.1023582
ID  - Baran2021
ER  -