Solitary wave solutions to the Isobe‐Kakinuma model for water waves. Issue 1 (22nd May 2020)

• Record Type: Journal Article
• Authors: Colin, Mathieu; Iguchi, Tatsuo
• Is Part Of: Studies in applied mathematics. Volume 145:Issue 1(2020)
• Page Start: 52
• Page End: 80
• Publication Date: 2020-05-22
• Subjects: fluid dynamics -- nonlinear waves -- partial differential equations -- water waves; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12310
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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.