一类奇摄动Kdv-Burgers方程与孤波解  

A Class of Singularly Perturbed Kdv-Burgers Equations and Solitary Wave Solutions

作　　者：李瑞翔 包立平[1] 吴立群 LI Ruixiang;BAO Liping;WU Liqun(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）》2020年第4期87-90,共4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：讨论一类奇摄动Kdv-Burgers方程,构造了对应小参数的零次近似解。首先,用黎曼-厄肖恩方法求得外解,得到简单波;其次,用行波法求内解,得到了孤子解;最后,构造相应的算子,用有界逆算子的性质得到解的一致有效性。In this paper, a class of singularly perturbed Kdv-Burgers equations is discussed, and a zero-order approximate solution for corresponding small parameters is constructed. Firstly, the Riemann-Earshawn method is used to find the external solution, the simple wave is obtained;Then, solving internal solutions by traveling wave method, the soliton solution is also obtained;Finally, the remainder is estimated by existence of uniformly bounded inverse operators, and the uniform validity of the asymptotic solution of the system is obtained.

关 键 词：KDV-BURGERS方程 孤波解 一致有效性 

分 类 号：O175.29[理学—数学]