Journal of Nonlinear Mathematical Physics

Volume 18, Issue 1, March 2011, Pages 9 - 28

Non-Isospectral 1+1 Hierarchies Arising from a Camassa Holm Hierarchy in 2+1 Dimensions

Authors
P. G. Estévez*, J. D. Lejarreta, C. Sardón
Departamento de Fisica Fundamental, Universidad de Salamanca, Salamanca, 37008, Spain
Corresponding Author
P. G. Estévez
Received 10 March 2010, Accepted 11 May 2010, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S140292511100112XHow to use a DOI?
Keywords
Lie symmetries, reductions, Camassa–Holm hierarchy
Abstract

The non-isospectral problem (Lax pair) associated with a hierarchy in 2 + 1 dimensions that generalizes the well known Camassa–Holm hierarchy is presented. Here, we have investigated the non-classical Lie symmetries of this Lax pair when the spectral parameter is considered as a field. These symmetries can be written in terms of five arbitrary constants and three arbitrary functions. Different similarity reductions associated with these symmetries have been derived. Of particular interest are the reduced hierarchies whose 1 + 1 Lax pair is also non-isospectral.

Copyright
© 2011 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 1
Pages
9 - 28
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S140292511100112XHow to use a DOI?
Copyright
© 2011 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/).

Cite this article

TY  - JOUR
AU  - P. G. Estévez
AU  - J. D. Lejarreta
AU  - C. Sardón
PY  - 2021
DA  - 2021/01
TI  - Non-Isospectral 1+1 Hierarchies Arising from a Camassa Holm Hierarchy in 2+1 Dimensions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 9
EP  - 28
VL  - 18
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S140292511100112X
DO  - https://doi.org/10.1142/S140292511100112X
ID  - Estévez2021
ER  -