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2013 Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation
Andrew Gratien Johnpillai, Chaudry Masood Khalique
Abstr. Appl. Anal. 2013(SI48): 1-5 (2013). DOI: 10.1155/2013/204746

Abstract

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.

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Andrew Gratien Johnpillai. Chaudry Masood Khalique. "Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation." Abstr. Appl. Anal. 2013 (SI48) 1 - 5, 2013. https://doi.org/10.1155/2013/204746

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1293.35015
MathSciNet: MR3102716
Digital Object Identifier: 10.1155/2013/204746

Rights: Copyright © 2013 Hindawi

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