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Acta Applicandae Mathematicae

, Volume 101, Issue 1–3, pp 231–241 | Cite as

Cartan’s Structure Theory of Symmetry Pseudo-Groups, Coverings and Multi-Valued Solutions for the Khokhlov–Zabolotskaya Equation

  • Oleg I. Morozov
Article

Abstract

We derive two non-equivalent coverings for the modified Khokhlov–Zabolotskaya equation from Maurer–Cartan forms of its symmetry pseudo-group. Also we find Bäcklund transformations between the obtained covering equations. We apply these results to constructing multi-valued solutions for the Khokhlov–Zabolotskaya equation.

Keywords

Lie pseudo-groups Maurer–Cartan forms Symmetries of differential equations Coverings of differential equations 

Mathematics Subject Classification (2000)

58H05 58J70 35A30 

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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Moscow State Technical University of Civil AviationMoscowRussia

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