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A Hamiltonian Structure of the Isobe–Kakinuma Model for Water Waves

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Abstract

We consider the Isobe–Kakinuma model for water waves, which is obtained as the system of Euler–Lagrange equations for a Lagrangian approximating Luke’s Lagrangian for water waves. We show that the Isobe–Kakinuma model also enjoys a Hamiltonian structure analogous to the one exhibited by V. E. Zakharov on the full water wave problem and, moreover, that the Hamiltonian of the Isobe–Kakinuma model is a higher order shallow water approximation to the one of the full water wave problem.

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Authors and Affiliations

  1. Institut de Recherche Mathématique de Rennes, Univ Rennes, CNRS, IRMAR-UMR 6625, 35000, Rennes, France

    Vincent Duchêne

  2. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Tatsuo Iguchi

Authors
  1. Vincent Duchêne
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  2. Tatsuo Iguchi
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Correspondence to Tatsuo Iguchi.

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The authors declare that they have no conflict of interest.

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Dedicated to the late Professor Walter L. Craig.

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T. I. was partially supported by JSPS KAKENHI Grant Number JP17K18742 and JP17H02856.

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Duchêne, V., Iguchi, T. A Hamiltonian Structure of the Isobe–Kakinuma Model for Water Waves. Water Waves 3, 193–211 (2021). https://doi.org/10.1007/s42286-020-00025-x

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