| BBM方程的Hamilton表示 |
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| 引用本文： | 张宏亮,张宝善. BBM方程的Hamilton表示[J]. 江苏大学学报(自然科学版), 2005, 26(Z1): 23-25 |
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| 作者姓名： | 张宏亮 张宝善 |
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| 作者单位： | 1. 徐州师范大学数学系,江苏,徐州,221116
2. 南京审计学院应用数学系,江苏,南京,210029 |
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| 基金项目： | 南京审计学院科研基金资助项目(NSK2005/B01) |
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| 摘 要： | 研究了水波动力学中重要规则长波方程之一的BBM方程的Hamilton表示.运用Olver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Hamilton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Hamilton表示.两种形式的Hamilton表示均可引进辛差分格式,进行数值解计算.
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| 关 键 词： | BBM方程 Hamilton形式 变分原理 |
| 文章编号： | 1671-7775(2005)06A-0023-3 |
| 修稿时间： | 2005-03-25 |
Hamilton''''s formal system on the BBM equation |
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| ZHANG Hong-liang,ZHANG Bao-shan. Hamilton''''s formal system on the BBM equation[J]. Journal of Jiangsu University:Natural Science Edition, 2005, 26(Z1): 23-25 |
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| Authors: | ZHANG Hong-liang ZHANG Bao-shan |
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| Affiliation: | ZHANG Hong-liang~1,ZHANG Bao-shan~2 |
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| Abstract: | 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. |
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| Keywords: | BBM equation Hamilton formula variable principle |
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