|本期目录/Table of Contents|

圆盘域波动方程基于Hamilton体系的分离变量法(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2015年06期
页码:
582-586
栏目:
研究论文
出版日期:
2015-11-20

文章信息/Info

Title:
A Method of Separation of Variables Based on the Hamiltonian System for Wave Equations in Circular Domains
作者:
秦伟 侯国林
内蒙古大学数学科学学院, 呼和浩特 010021
Author(s):
QIN Wei HOU Guo-lin
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
关键词:
Hamilton系统Bessel函数完备性
Keywords:
Hamiltonian systemBessel functioncompletenesssolution
分类号:
O175.3
DOI:
-
文献标识码:
-
摘要:
对于极坐标系下的波动方程,首先通过引入合适的对偶变量将其化为Hamilton系统,并基于Bessel函数的性质证明了导出的Hamilton算子矩阵本征函数系的完备性定理,最后利用展开定理给出了Hamilton系统的解.
Abstract:
The wave equation in the polar coordinates is firstly derived to the Hamiltonian system by choosing the appropriate dual variable.Moreover,a completeness theorem of the eigenfunction system for the Hamiltonian operator is proved by the properties of Bessel functions.Finally,the solution of the Hamiltonian system is given by the expansion theorem.

参考文献/References

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备注/Memo

备注/Memo:
收稿日期:2015-04-13;改回日期:。
基金项目:国家自然科学基金(11361034);内蒙古自然科学基金(2012MS0105);内蒙古自治区高等学校青年科技英才支持计划(NJYT-15-B03)
作者简介:秦伟(1988-),女,内蒙古乌兰察布人,硕士.研究方向:算子矩阵及其应用.
通讯作者:侯国林(1980-),男,内蒙古呼伦贝尔人,教授,博士.E-mail:smshgl@imu.edu.cn.
更新日期/Last Update: 1900-01-01