摘要
基于Hamilton空间体系下的多辛降阶理论构造了广义五阶KdV方程的一阶对称形式,随后证明了该对称形式是多辛的,最后应用多辛理论研究了广义五阶KdV方程的多种局部守恒律,为高阶发展方程的固有几何性质研究提供了新的途径。
Aim. Many special properties of the evolution equations are derived from their symmetry as well as from their local conservation laws. We now utilize the developing theory of muhi-symplecticity to study the inner properties of the generalized fifth order KdV equation. Sections 1 and 2 of the full paper explain our explorative research in some detail. In addition to briefing past research, the core of section 1 is that we derive eq. （9） as the first order symmetric form for the generalized fifth order KdV equation by introducing the momentum series eq. （7）. The core of section 2 consists of： （1） we prove that the symmetric form eq. （9） satisfies the multi-symplectic conservation law eq. （10） recurring to the outer product; （2） using the muhi-symplectic theory, we derive the local energy con- servation law eq. （17） and the local momentum conservation law eq. （19） ; they express the local properties of the generalized fifth order KdV equation. The results of this paper appear to allow studying the geometric properties of the high order evolution equation in a new way.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2011年第4期594-597,共4页
Journal of Northwestern Polytechnical University
基金
国家自然科学基金(10972182
11002115和10972125)
111引智计划(B07050)
航空科学基金(2010ZB53021)
西北工业大学基础研究基金(JC200938)
高校博士点基金(20106102110019)
机械系统与振动国家重点实验室开放课题(MSV-2011-21)
大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助
关键词
广义五阶KDV方程
局部守恒律
对称性
energy conservation, geometry, generalized fifth order KdV equation, symmetry
