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Zeitschrift für Naturforschung A Contents Vol. 67a (2012)

Z. Naturforsch. 67a, 613 – 620 (2012)

doi:10.5560/ZNA.2012-0071

Soliton Solutions, Conservation Laws, and Reductions of Certain Classes of Nonlinear Wave Equations

Richard Morris¹, Abdul Hamid Kara¹, Abhinandan Chowdhury², and Anjan Biswas²

¹School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

²Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA

Received May 10, 2012 / revised June 28, 2012 / published online September 19, 2012

Reprint requests to: A. B.; E-mail: biswas.anjan@gmail.com

In this paper, the soliton solutions and the corresponding conservation laws of a few nonlinear wave equations will be obtained. The Hunter–Saxton equation, the improved Korteweg–de Vries equation, and other such equations will be considered. The Lie symmetry approach will be utilized to extract the conserved densities of these equations. The soliton solutions will be used to obtain the conserved quantities of these equations.

Key words: Lie Symmetries; Conservation Laws; Double Reduction.

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