A Hamiltonian structure of the {I}sobe-{K}akinuma model for water waves

Vincent Duchêne (1) , Tatsuo Iguchi (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 KEIO UNIVERSITY - Department of Mathematics

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.

Mots clés: Water waves; Shallow water models; Hamiltonian structure

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Duchêne, Tatsuo Iguchi. A Hamiltonian structure of the {I}sobe-{K}akinuma model for water waves. Water Waves, 2021, 3 (1), pp.193-211. ⟨10.1007/s42286-020-00025-x⟩. ⟨hal-02299441⟩