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arXiv · 1910.01026

A Hamiltonian structure of the Isobe-Kakinuma model for water waves

Vincent Duchêne·Tatsuo Iguchi
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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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Vincent Duchêne, Tatsuo Iguchi. 2019-10-01. A Hamiltonian structure of the Isobe-Kakinuma model for water waves. https://doi.org/10.1007/s42286-020-00025-x

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