Journal of Nonlinear Mathematical Physics

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Volume 16, Issue 2, June 2009, Pages 169 - 178

Commutativity of Pfaffianization and Bäcklund Transformations: The Leznov Lattice

Authors
Chun-Xia Li
School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China,trisha-li2001@yahoo.com
Jun-Xiao Zhao
School of Mathematical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, P. R. China
Institute of Applied Physics and Computational Mathematics, P. O. Box 8009/28, Beijing 100088, P. R. China,jxzhao@gucas.ac.cn
Xing-Biao Hu
Institute of Computational Mathematics, and Scientific Engineering Computing, AMSS, Academia Sinica, P. O. Box 2719, Beijing 100029, P. R. China,hxb@lsec.cc.ac.cn
Received 20 March 2008, Accepted 14 November 2008, Available Online 7 January 2021.
DOI
10.1142/S1402925109000169How to use a DOI?
Keywords
The coupled Leznov lattice; Pfaffianization; Bäcklund transformation; Wronskian; pfaffian
Abstract

In this paper, we first obtain Wronskian solutions to the Bäcklund transformation of the Leznov lattice and then derive the coupled system for the Bäcklund transformation through Pfaffianization. It is shown the coupled system is nothing but the Bäcklund transformation for the coupled Leznov lattice introduced by J. Zhao etc. [1]. This implies that Pfaffianization and Bäcklund transformation is commutative for the Leznov lattice. Moreover, since the two-dimensional Toda lattice constitutes the Leznov lattice, it is obvious that the commutativity is also valid for it.

Copyright
© 2009 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
16 - 2
Pages
169 - 178
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925109000169How to use a DOI?
Copyright
© 2009 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

risenwbib
TY  - JOUR
AU  - Chun-Xia Li
AU  - Jun-Xiao Zhao
AU  - Xing-Biao Hu
PY  - 2021
DA  - 2021/01/07
TI  - Commutativity of Pfaffianization and Bäcklund Transformations: The Leznov Lattice
JO  - Journal of Nonlinear Mathematical Physics
SP  - 169
EP  - 178
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000169
DO  - 10.1142/S1402925109000169
ID  - Li2021
ER  -