BBM方程的Hamilton表示

Hamilton's formal system on the BBM equation

研究了水波动力学中重要规则长波方程之一的BBM方程的Ham ilton表示.运用O lver研究该类方程的守恒律来定义能量函数E(u),推导出一种新型的变分原理,并利用所得到的变分原理导出BBM方程的Ham ilton表示.同时,利用待定泛函形式的变分原理导出另一种形式的BBM方程的Ham ilton表示.两种形式的Ham ilton表示均可引进辛差分格式,进行数值解计算.

it is well known that the BBM equation is an important regular equation with long wave. The Hamilton＇s formal system for the BBM equation is concerned. An energetic function E（u） based on the conservation laws in nonlinear water-waves as Olver＇s work is defined, and a new variable principle is obtained. Using this variable principle, the Hamiltonian formulation of BBM equation is conducted. Meanwhile, another Hamiltonian formulation of BBM equation is obtained through an undetermined functional variable principle. Both formulas of the Hamilton＇s formal system can be used to get the symplectic transformation and the numerical computations.