A SHOOTING METHOD FOR THE SWIFT-HOHENBERG EQUATION  

作　　者：TaoYoushan ZhangJizhou 

机构地区：[1]Dept.ofAppl.Math.,DonghuaUniv.,Shanghai200051.China [2]CollegeofMath.Sci.,ShanghaiNormalUniv.,Shanghai200234,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2002年第4期391-403,共13页高校应用数学学报（英文版）（B辑）

基　　金：National Natural Science Foundation of China (1 0 0 71 0 67)

摘　　要：Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<32 , there exist periodic solutions having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<32 , there exist periodic solutions having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.

关 键 词：shooting technique Swift  Hohenberg equation critical point periodic solution. 

分 类 号：O175[理学—数学]