标题： 哈密顿模型用于长重力波的传播，高阶KdV型方程和可积性 显示英文标题

标题： Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability

摘要： 一个被自由表面包围的不可压缩、无粘性、无旋流体介质被考虑。 系统的哈密顿量用所谓的狄利克雷-诺伊曼算子来表示。 表面波的方程以哈密顿形式给出。 选择了特定的变量缩放，导致具有高阶非线性和色散的KdV近似（高阶KdV型方程，或HKdV）。 HKdV与已知的可积偏微分方程通过显式非线性和非局部变换相关联。 显示英文摘要

摘要： A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation.