Solitary wave solutions to the Isobe-Kakinuma model for water waves

Abstract

We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of the flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show theoretically the existence of a family of small amplitude solitary wave solutions to the Isobe-Kakinuma model in the long wave regime. Numerical analysis for large amplitude solitary wave solutions is also provided and suggests the existence of a solitary wave of extreme form with a sharp crest.

25 pages, 6 figures

References in corpus (4)

• Isobe-Kakinuma model for water waves as a higher order shallow water approximation
• 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
• A Hamiltonian structure of the Isobe-Kakinuma model for water waves