CH-KP方程的哈密顿方法
A Hamiltonian approach to the CH-KP equation
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中文总结 AI 辅助
从欧拉方程推导浅水层准单向波传播模型，得到CH-KP方程，其哈密顿结构由狄拉克约化得到，极限情况可简化为CH方程，给出弱peakon型解说明其碰撞行为。
中文摘要 AI 辅助
从欧拉方程出发，结合长波渐近分析与哈密顿约化技术，推导得到描述浅水层表面准单向波传播的模型。研究了非线性、色散以及对第二平面坐标的弱依赖之间的平衡，由此得到所谓的CH-KP方程，这是著名的Kadomtsev-Petviashvili方程的轻度非线性版本。该模型的哈密顿结构通过从分层流体全非线性长波系统的中间步骤进行狄拉克约化得到。考虑了一种特定标度，该标度在极限情况下将此类系统简化为一维CH方程。提供了弱peakon型解的例子，这些解被选来说明极限方程所支持的碰撞行为。
英文摘要
A model governing quasi-unidirectional wave propagation at the surface of a shallow layer of water is derived from Euler equations by long wave asymptotics together with Hamiltonian reduction techniques. The balance between nonlinearity, dispersion and weak dependence on the second planar coordinate is examined and results in the so-called CH-KP equation, a mildly nonlinear version of the well known Kadomtsev-Petviashvili equation. The Hamiltonian structure of the model is obtained by Dirac reduction from the intermediate step of a fully-nonlinear, long-wave system for stratified fluids. A particular scaling is considered that reduces such system to the one-dimensional CH equation in a limiting case. Examples of weak peakon-type solutions are provided, chosen to illustrate the collision behavior supported by the limiting equation.
