Journal of Nonlinear Mathematical Physics

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Volume 21, Issue 3, June 2014, Pages 454 - 472

Nonlocal symmetry constraints and exact interaction solutions of the (2+1) dimensional modified generalized long dispersive wave equation

Authors
Junchao Chen
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, People's Republic of China
Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78541, USA
Yong Chen*
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, People's Republic of China,ychen@sei.ecnu.edu.cn
*Corresponding author.
Corresponding Author
Yong Chen
Received 7 March 2014, Accepted 29 May 2014, Available Online 6 January 2021.
DOI
10.1080/14029251.2014.936764How to use a DOI?
Keywords
(2+1) dimensional modified generalized long dispersive equation; nonlocal symmetry; localization; nonlocal symmetry constraint; exact interaction solutions
Abstract

In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials, the prolongation is found to localize the given nonlocal symmetry. Various finite-and infinite-dimensional integrable models are constructed by using the nonlocal symmetry constraint method. Moreover, applying the general Lie symmetry approach to the enlarged system, the finite symmetry transformation and similarity reductions are computed to give novel exact interaction solutions. In particular, the explicit soliton-cnoidal wave solution is obtained for the modified generalized long dispersive wave system, and it can be reduced to the two-dark-soliton solution in one special case.

Copyright
© 2014 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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<Previous Article In Issue
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 3
Pages
454 - 472
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2014.936764How to use a DOI?
Copyright
© 2014 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  - Junchao Chen
AU  - Yong Chen
PY  - 2021
DA  - 2021/01/06
TI  - Nonlocal symmetry constraints and exact interaction solutions of the (2+1) dimensional modified generalized long dispersive wave equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 454
EP  - 472
VL  - 21
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.936764
DO  - 10.1080/14029251.2014.936764
ID  - Chen2021
ER  -