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arXiv · 1910.06481

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

Mathieu Colin·Tatsuo Iguchi
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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.

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Mathieu Colin, Tatsuo Iguchi. 2019-10-15. Solitary wave solutions to the Isobe-Kakinuma model for water waves. https://doi.org/10.1111/sapm.12310

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