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.

中文翻译：

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Isobe-Kakinuma 水波模型的孤立波解

我们考虑平底情况下二维水波的 Isobe-Kakinuma 模型。Isobe-Kakinuma 模型是一个拉格朗日方程的欧拉-拉格朗日方程系统，它近似于水波的卢克拉格朗日方程。我们从理论上证明了在长波状态下 Isobe-Kakinuma 模型的一系列小振幅孤立波解的存在。还提供了大振幅孤立波解的数值分析，并表明存在具有尖锐波峰的极端形式的孤立波。