The Short Pulse Equation – a symmetry study

Article type: Research Article

Authors: Huber, Alfred

Affiliations: Prottesweg 2a, A-8062 Kumberg, Austria. E-mail: soliton.alf@web.de

Abstract: The classical Lie group formalism is applied to deduce classes of solutions of a special nonlinear partial differential equation, the so called Short-Pulse-Equation important in physical applications. We determine the Lie point symmetries and their algebraic properties. Similarity solutions are given as well as nonlinear transformations. In addition we discuss approximate symmetries for the first time. This analysis allows one to deduce wider classes of new unknown solutions either of practical or theoretical use.

Keywords: Nonlinear partial differential equations, evolution equations, Short-Pulse-Equation, similarity solutions, approximate symmetries

DOI: 10.3233/JCM-2010-0262

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 1-2, pp. 79-87, 2010