Solitary wave solutions to the Isobe‐Kakinuma model for water waves
Copyright policy )Solitary wave solutions to the Isobe‐Kakinuma model for water waves
AbstractWe 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.
water waves, nonlinear waves, fluid dynamics, PDEs in connection with fluid mechanics, Solitary waves for incompressible inviscid fluids, Mathematics - Analysis of PDEs, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, partial differential equations, FOS: Mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
water waves, nonlinear waves, fluid dynamics, PDEs in connection with fluid mechanics, Solitary waves for incompressible inviscid fluids, Mathematics - Analysis of PDEs, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, partial differential equations, FOS: Mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
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