一类广义非线性强阻尼扰动发展方程的行波解

冯依虎; 石兰芳; 汪维刚; 莫嘉琪

doi:10.3879/j.issn.1000-0887.2015.03.009

一类广义非线性强阻尼扰动发展方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.03.009

¹亳州师范高等专科学校理工系, 安徽亳州 236800;²南京信息工程大学数学与统计学院, 南京 210044;³安庆师范学院桐城教学部, 安徽桐城 231402;⁴安徽师范大学数学系, 安徽芜湖241003

基金项目: 国家自然科学基金(11202106)

详细信息

作者简介:
冯依虎（1982—），男，安徽潜山人，讲师，硕士(E-mail: fengyihubzsz@163.com);莫嘉琪（1937—），男，浙江德清人，教授（通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn）.

中图分类号: O175.29
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出版历程
- 收稿日期: 2014-11-19
- 修回日期: 2014-12-11
- 刊出日期: 2015-03-15

Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations

¹Department of Science and Technology, Bozhou Teachers College, Bozhou, Anhui 236800, P.R.China;²College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China;³Tongcheng Teaching Department, Anqing Normal University, Tongcheng, Anhui 231402, P.R.China;⁴Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

摘要

摘要: 研究了一类非线性强阻尼广义扰动发展方程问题.它们在数学、力学、物理学等领域中广泛出现.首先，引入一个行波变换，把相应的偏微分方程问题转化为行波方程问题并求出原典型问题的精确解.再用小参数方法和引入伸长变量构造了问题的渐近解.最后, 用泛函分析的不动点理论证明了原非线性强阻尼广义扰动发展方程初值问题渐近行波解的存在性，并证明渐近解具有较高的精度和一致有效性.该文求得的渐近解是一个解析展开式, 所以它还可继续进行解析运算, 而单纯用数值模拟的方法是不行的.
- 行波 /
- 强阻尼 /
- 发展方程
Abstract: A class of generalized nonlinear strong-damp disturbed evolution differential equations were studied, which widely appeared in the fields of mathematics, mechanics and physics etc.. Firstly, a travelling wave transformation was introduced to convert the related problem of partial differential equations to one of travelling wave equations, with the exact solution to the original typical problem obtained. Then the small parameter method was used and the stretched variables introduced to construct the asymptotic solution. Finally, the existence, high accuracy and uniform validity of the asymptotic travelling wave solution to the original generalized nonlinear strong-damp disturbed evolution equation for the initial-value problem were proved with the fixed point theory for functional analysis. The presented travelling wave asymptotic solution is an analytic expansion, therefore, it is continuously open to analytic operations, which reject the solutions given by those pure numerical methods.
- travelling wave /
- strong damp /
- evolution equation

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参考文献(21)

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一类广义非线性强阻尼扰动发展方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.03.009

作者简介:
冯依虎（1982—），男，安徽潜山人，讲师，硕士(E-mail: fengyihubzsz@163.com);莫嘉琪（1937—），男，浙江德清人，教授（通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn）.

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Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations

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留言板

一类广义非线性强阻尼扰动发展方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.03.009

作者简介: 冯依虎（1982—），男，安徽潜山人，讲师，硕士(E-mail: fengyihubzsz@163.com);莫嘉琪（1937—），男，浙江德清人，教授（通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn）.

计量

出版历程

Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations

计量

出版历程

目录

作者简介:
冯依虎（1982—），男，安徽潜山人，讲师，硕士(E-mail: fengyihubzsz@163.com);莫嘉琪（1937—），男，浙江德清人，教授（通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn）.