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第四类Painlevé方程解的渐近性态分析 被引量：2

Analysis of asymtotics of general fourth Painlevé equation
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摘要 近年来关于Painlev啨方程解的渐近性态有了许多结果,但对第四类Painlev啨　　y″=y′22y+32y3+4xy2+2(x2-α)y+βy方程解的渐近性态的研究并不多.给出一类振荡渐近解的表达形式:　　y=-23x+Bcos(33x2+bln|x|+c)+O(|x|-1),x→±∞. There are many results on the asymptotics of the Painlevé transcendents in recent years, but the asymptotics of the fourth Painlevé transcendent has not almost been studied.The form of expression of the asymptotics vibrational solutiony=-23x+Bcos(33x^2+bln｜x｜+c)+O(｜x｜^(-1)),x→±∞, is given for the fouth Plainlevé equation:y″=y′~22y+32y^3+4xy^2+2(x^2-α)y+βy.
作者 秦惠增 商妮娜
机构地区 山东理工大学数学与信息科学学院
出处 《山东理工大学学报（自然科学版）》 CAS 2004年第2期12-15,共4页 Journal of Shandong University of Technology:Natural Science Edition
关键词 Painlevé方程解 渐近性态 振荡渐近解 中极值点 Painlevé equation vibrational solution asymptotics
分类号 O175.14 [理学—基础数学]
  • 相关文献

参考文献10

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  • 9商妮娜,秦惠增.第三类Painlevé方程解的渐近性态分析[J].山东理工大学学报（自然科学版）,2004,18(1):54-57. 被引量：3
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二级参考文献8

  • 1Ovldiu Costin, Rodica D. Costin Asymptotis Properties of a Family of Solutions of the Painlevé Equation[J]. IMRN, 2002,No. x.
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  • 8Mazzocco M. Rational Solutions to Painlevé VI equation[ J ]. nlin. Si/0007036, 2000,24:1-13.

共引文献2

同被引文献15

  • 1斯仁道尔吉.组合KDV方程的新的相似约化[J].内蒙古师范大学学报（自然科学汉文版）,1996,25(2):1-6. 被引量：3
  • 2郭玉翠,徐淑奖.描述顺流方向可变剪切流动的一类变系数Boussinesq方程的Painlevé分析和相似约化[J].应用数学学报,2006,29(6):1054-1062. 被引量：4
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  • 6Gamier R. Contributionia Petude des solutions de l'equation (V) de Painleve[J]. J. Math. Pures. Appl, 1967,46: 353-412.
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  • 8Shimomura S. On solutions of the fifth Painleve eqution on the positive real axis Ⅰ[J]. Funkcialaj Ekvacioj, 1985,28:341-370.
  • 9Hodyss D,Nathan T R. Phys Rev Lett,2004,93:074502--1--4.
  • 10Clarkson P A, Kruskal M D. New similarity reductions of Boussinesq equation [J]. J Math Phys, 1989,30:2 201--2 213.

引证文献2

山东理工大学学报（自然科学版）
2004年 第2期

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