Symmetry reductions, exact solutions, and conservation laws of a modified Hunter-Saxton equation
type: Item
instance of: scholarly article
title: Symmetry reductions, exact solutions, and conservation laws of a modified Hunter-Saxton equation
zbMATH Open document ID: 1293.35015
DOI: 10.1155/2013/204746
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation.
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 6306524
zbMATH Keywords: exact group-invariant traveling wave solutions
zbMATH Keywords: optimal system of one-dimensional subalgebras
zbMATH Keywords: nonlocal conservation laws
Wikidata QID: Q58915538
author: Andrew Gratien Johnpillai
author: Chaudry Masood Khalique
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/204746
OpenAlex ID: W2171818444
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description: scientific article; zbMATH DE number 6306524