组合KdV方程的孤立波解与相似解
Solitary Wave and Similarity Solutions of the Combined KdV Equation
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摘要: 本文讨论组合KdV方程孤立波解的一个性质,指出该方程可化为Painlevé方程,并利用相似变量的特殊变换导出一类新的偏微分方程.Abstract: In this paper,we discuss a property of solitary wave solutions of the combined KdV equation.Meantime,we point out that the combined KdV equation can be reduced to the Painleve equation.Furthermore,utilizing special transformations of similarity variables,we derive a kind of new partial differential equations.
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[1] Toda M.,Progr,Theor.Phys.Suppl.,45(1970) 174. [2] 戴世强,两层流体界面上的孤立波,应用数学和力学,3,6(1982),721-731. [3] Wadati Miki,Wave propagation in nonlinear lattice,Ⅰ.Ⅱ.,J.P.S.38,3 Japan(1975),673-686. [4] Ablowitz,M.J.and H.Segur,Phys.Rev.Lett.,38(1977),1103. [5] 王明亮,KdV-Burgers方程的孤立波解的性质,兰州大学学报,19,(1983),9-18. [6] Bluman,G.W.and J.D.Cole,Similarity,Methods for Differential Equation,Springer,Berlin(1974). -
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