A Hamiltonian structure of the Isobe-Kakinuma model for water waves
A Hamiltonian structure of the Isobe-Kakinuma model for water waves
复制标题
水波 Isobe-Kakinuma 模型的哈密顿结构
DOI：
10.1007/s42286-020-00025-x
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Vincent Duchene and Tatsuo Iguchi
中科院分区：
文献类型：
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作者：
Vincent Duchene and Tatsuo Iguchi
我们考虑水波的Isobe-Kakinuma模型，它是由欧拉-拉格朗日方程组得到的，其拉格朗日函数近似于水波的Luke拉格朗日函数。我们证明了Isobe-Kakinuma模型也具有类似于V.E.Zakharov关于全水波问题的哈密顿结构，而且Isobe-Kakinuma模型的哈密顿量是全水波问题的高阶浅水近似。
We consider the Isobe–Kakinuma model for water waves, which is obtained as the system of Euler–Lagrange equations for a Lagrangian approximating Luke’s Lagrangian for water waves. We show that the Isobe–Kakinuma model also enjoys a Hamiltonian structure analogous to the one exhibited by V. E. Zakharov on the full water wave problem and, moreover, that the Hamiltonian of the Isobe–Kakinuma model is a higher order shallow water approximation to the one of the full water wave problem.