一类奇摄动拟线性方程的钉子解  

Spike Solution of a Class of Singularly Perturbed Quasi-linear Equations

作　　者：李文彦 包立平[1] LI Wenyan;BAO Liping(Institute of Mathematics,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学数学研究所,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2018年第6期89-93,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(51775154)

摘　　要：讨论了一类带小参数的泛函最小元的奇摄动问题,其最小元满足Euler-Lagrange方程,即奇摄动二阶非线性边界问题。通过奇摄动分析,得到该问题的内解和外解。该问题的解在奇摄动分析中属于钉子解,在物理上代表孤立子。通过对内解的分析,应用雅氏椭圆函数完整地展示了该钉子解的基本结构,明确表达了孤立子的形态。In this paper,the singularly perturbed problem of a functional minimum element with small parameters is discussed.The minimum element satisfies the Euler-Lagrange equation,that is,the two order nonlinear boundary problem of singularly perturbed.By the singularly perturbed analysis,the internal and external solutions of the problem are obtained.The solution of the problem in perturbation analysis belongs to the spike solution and represents the soliton in physics.Through the analysis of the internal solution,the basic structure of the solution is fully demonstrated by using the Jahs elliptic function,and the form of the soliton is clearly expressed.

关 键 词：奇摄动 拟线性方程 钉子解 

分 类 号：O175.2[理学—数学]