Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach

DOI

10.1080/14029251.2015.1023562How to use a DOI?

Keywords

Dispersive long waves system; Lie symmetry; Conservation law; Nonlocally related systems; Geometric approach; Kac-Moody-Virasoro algebra

Abstract

By using the extended Harrison and Estabrook's differential forms approach, in this paper, we investigate the Lie symmetries of the continuous and discrete dispersive long waves system, respectively. Based on this method, two closed ideals written in terms of a set of differential forms are constructed for the dispersive long waves systems. Furthermore, some invariant solutions are presented for such systems. By a direct computation, it is shown that the discrete dispersive long waves system admits a Kac-Moody-Virasoro type and a Virasoro-like type Lie algebra, respectively. Finally, we present an interesting relationship between the continuous case and a modified dispersive long waves system, which can be used to find nonlocal properties for such systems with each other.

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  - Shou-Fu Tian
AU  - Tian-Tian Zhang
AU  - Pan-Li Ma
AU  - Xing-Yong Zhang
PY  - 2021
DA  - 2021/01/06
TI  - Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach
JO  - Journal of Nonlinear Mathematical Physics
SP  - 180
EP  - 193
VL  - 22
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.1023562
DO  - 10.1080/14029251.2015.1023562
ID  - Tian2021
ER  -