一类广义非线性强阻尼扰动发展方程的行波解  

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

作　　者：冯依虎[1] 石兰芳[2] 汪维刚 莫嘉琪[4] 

机构地区：[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

出　　处：《应用数学和力学》2015年第3期315-324,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202106)~~

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.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.

关 键 词：行波 强阻尼 发展方程 

分 类 号：O175.29[理学—数学]