具有阻尼项的非线性波动方程的相似约化

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u_tt-2bu_xxt+αu_xxxx=β(uⁿ_x)x(α>0,β≠0,n≥2)三种类型的相似约化.从这些约化方程的Painlevé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4种精确类孤波解. 关键词： 波动方程 相似约化 Painlevé分析 精确解

SIMILARITY REDUCTIONS FOR A NONLINEAR WAVE EQUATION WITH DAMPING TERM

Three types of similarity reductions are obtained for nonlinear wave equation with damping term u_tt-2bu_xxt+αu_xxxx=β(uⁿ_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).