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

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.

arXiv admin note: text overlap with arXiv:1803.09236

References in corpus (3)

• On the Hamiltonian for water waves
• A mathematical justification of the Isobe-Kakinuma model for water waves with and without bottom topography
• Solvability of the initial value problem to the Isobe-Kakinuma model for water waves

Cited by in corpus (3)

• Solitary wave solutions to the Isobe-Kakinuma model for water waves
• A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: Justification as a shallow water approximation
• A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness