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

We consider the Isobe‐Kakinuma model for two‐dimensional water waves in the case of a 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 amplitud...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2020-07, Vol.145 (1), p.52-80
Main Authors: Colin, Mathieu, Iguchi, Tatsuo
Format: Article
Language:English
Subjects:
Amplitudes
Analysis of PDEs
Euler-Lagrange equation
fluid dynamics
Mathematics
nonlinear waves
Numerical analysis
partial differential equations
Solitary waves
Water waves
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Summary:We consider the Isobe‐Kakinuma model for two‐dimensional water waves in the case of a 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.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12310