Higher Painleve transcendents as special solutions of some nonlinear integrable hierarchies

被引：19

作者：

Kudryashov, Nikolay A. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPhI, Dept Appl Math, Moscow 115409, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2014年 / 19卷 / 01期

关键词：

Painleve equation; Painleve transcendent; Korteweg-de Vries hierarchy; modified Korteveg-de Vries hierarchy; Kaup-Kupershmidt hierarchy; Caudrey-Dodd-Cibbon hierarchy; ORDINARY DIFFERENTIAL-EQUATIONS; YABLONSKII-VOROBEV POLYNOMIALS; HIGHER-ORDER; POINT VORTICES; 2ND; 1ST; TRANSFORMATIONS; 2ND-PAINLEVE; EVOLUTION; SOLITON;

D O I：

10.1134/S1560354714010043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that the self-similar solutions of the Korteweg-de Vries equation and the modified Korteweg-de Vries equation are expressed via the solutions of the first and second Painlev, equations. In this paper we solve this problem for all equations from the Korteveg-de Vries, modified Korteweg-de Vries, Kaup-Kupershmidt, Caudrey-Dodd-Gibbon and Fordy-Gibbons hierarchies. We show that the self-similar solutions of equations corresponding to hierarchies mentioned above can be found by means of the general solutions of higher-order Painlev, hierarchies introduced more than ten years ago.

引用

页码：48 / 63

页数：16

共 66 条

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