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Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems

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Solitons

Part of the book series: Springer Series in ((SSNONLINEAR))

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Abstract

Recent developments by the authors in finding the recursion operators and the bi-Hamiltonian formulation of a large class of nonlinear evolution equations in (2+1)-dimensions is reviewed. The general theory associated with factorizable recursion operators in multidimensions is discussed. Both gradient and non-gradient master-symmetries are simply derived and their general theory is developed, using the Kadomtsev-Petviashvili equation as an example.

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Author information

Author notes

  1. P. M. Santini

    Present address: Istituto di Fisica “Guglielmo Marconi”, Universitá Degli Studi, Roma, Piazzale delle Scienze, 5, I-1-00185, Roma, Italy

Authors and Affiliations

  1. Department of Mathematics and Computer Science and Institute for Nonlinear Studies, Clarkson University, Potsdam, NY, 13676, USA

    A. S. Fokas & P. M. Santini

Authors
  1. A. S. Fokas
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  2. P. M. Santini
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Editor information

Editors and Affiliations

  1. Department of Physics, Bharathidasan University, Tiruchirapalli, 620 024, Tamil Nadu, India

    Muthusamy Lakshmanan

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© 1988 Springer-Verlag Berlin Heidelberg

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Fokas, A.S., Santini, P.M. (1988). Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems. In: Lakshmanan, M. (eds) Solitons. Springer Series in Nonlinear Dynamics . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73193-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-73193-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73195-2

  • Online ISBN: 978-3-642-73193-8

  • eBook Packages: Springer Book Archive

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