Symmetry analysis of a system of modified shallow-water equations

2012/12/23 by Szatmari, Simon, Bihlo, Alexander
#Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1212.5823

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.

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