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Mathematics of dispersive water waves

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Abstract

A commuting hierarchy of dispersive water wave equations makes a three-Hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed. The modified water wave hierarchy is a bi-Hamiltonian system; its modification bifurcates. The water wave hierarchy, and the hierarchies of the Korteweg-de Vries and the modified Korteweg-de Vries equations, as well as the classical Miura map, are given new representations through various specializations of nonstandard systems.

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Authors and Affiliations

  1. The University of Tennessee Space Institute, 37388, Tullahoma, TN, USA

    B. A. Kupershmidt

  2. Center for Nonlinear Studies, Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    B. A. Kupershmidt

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  1. B. A. Kupershmidt
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Communicated by L. Nirenberg

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Kupershmidt, B.A. Mathematics of dispersive water waves. Commun.Math. Phys. 99, 51–73 (1985). https://doi.org/10.1007/BF01466593

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  • DOI: https://doi.org/10.1007/BF01466593

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