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Ermakov Structure in 2 + 1-Dimensional Systems. Canonical Reduction

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Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics

Abstract

Ermakov-type systems in 2 + 1-dimensions are introduced. Multi-wave solutions of a 2 + 1-dimensional Pinney equation and a modulated 2 + 1-dimensional sine-Gordon equation are constructed via the standard Ermakov system. Lie group analysis of the latter is undertaken to reveal its underlying linear structure in terms of canonical coordinates. In conclusion, a 2 + 1-dimensional nonlinear system due to Stoker which arises in two-layer shallow water theory is shown to admit a symmetry reduction to a Ermakov system.

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Author notes

  1. C. Rogers

    Present address: Department of Applied Mathematics, University of New South Wales, Australia

Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University of Technology, UK

    C. Rogers, C. Hoenselaers & U. Ramgulam

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  1. C. Rogers
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  2. C. Hoenselaers
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  3. U. Ramgulam
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Catania, Catania, Italy

    N. H. Ibragimov , M. Torrisi  & A. Valenti ,  & 

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© 1993 Springer Science+Business Media Dordrecht

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Rogers, C., Hoenselaers, C., Ramgulam, U. (1993). Ermakov Structure in 2 + 1-Dimensional Systems. Canonical Reduction. In: Ibragimov, N.H., Torrisi, M., Valenti, A. (eds) Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2050-0_34

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  • DOI: https://doi.org/10.1007/978-94-011-2050-0_34

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4908-5

  • Online ISBN: 978-94-011-2050-0

  • eBook Packages: Springer Book Archive

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