具有阻尼项的非线性波动方程的相似约化  

SIMILARITY REDUCTIONS FOR A NONLINEAR WAVE EQUATION WITH DAMPING TERM

作　　者：闫振亚[1] 张鸿庆[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《物理学报》2000年第11期2113-2117,共5页Acta Physica Sinica

基　　金：国家重点基础研究发展规划!(批准号 :G19980 3 0 60 0 );高等学校博士学科点专项科研基金!(批准号 :980 14 119)资助的课题&&

摘　　要：利用Clarkson和Kruskal引入的直接约化法 ,给出了具有阻尼项的非线性波动方程utt- 2buxxt+αuxxxx=β(unx) x(α >0 ,β≠ 0 ,n≥ 2 )三种类型的相似约化 .从这些约化方程的Painlev啨分析表明该方程在Ａｂｌｏｗｉｔｚ的猜测意义下是不可积的 .此外还获得了该方程 (n =2 )的Three types of similarity reductions are obtained for nonlinear wave equation with damping term u tt -2bu xxt +αu xxxx =β(u n x) x(α>0,β≠0,n≥2) by the use of the direct reduction method due to Clarkson and Kruskal.It is shown that this equation is not integrable under the sense of Ablowitz's conjecture by analysing the Painlevé properties of these reduction equations.In addition,four families of exact solutions are found for this equation( n=2 ).

关 键 词：相似约化 精确解 非线性波动方程 阻尼项 

分 类 号：O411.1[理学—理论物理]