Symmetry analysis of a system of modified shallow-water equations
Mathematical Physics
2012-12-27 v1 Analysis of PDEs
math.MP
Atmospheric and Oceanic Physics
Fluid Dynamics
Abstract
We revise the symmetry analysis of a modified system of one-dimensional shallow-water equations (MSWE) recently considered by Raja Sekhar and Sharma [Commun. Nonlinear Sci. Numer. Simulat. 20 (2012) 630-636]. Only a finite dimensional subalgebra of the maximal Lie invariance algebra of the MSWE, which in fact is infinite dimensional, was found in the aforementioned paper. The MSWE can be linearized using a hodograph transformation. An optimal list of inequivalent one-dimensional subalgebras of the maximal Lie invariance algebra is constructed and used for Lie reductions. Non-Lie solutions are found from solutions of the linearized MSWE.
Keywords
Cite
@article{arxiv.1212.5823,
title = {Symmetry analysis of a system of modified shallow-water equations},
author = {Simon Szatmari and Alexander Bihlo},
journal= {arXiv preprint arXiv:1212.5823},
year = {2012}
}
Comments
10 pages