Parametric Painlevé equations

被引：0
|
作者：
Kitaev A.V. [1 ]
机构：
[1] St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg
来源：
Journal of Mathematical Sciences | 2013年 / 192卷 / 1期
关键词：
General Solution; Short Pulse; Analytic Property; Parametric Form; Similarity Solution;
D O I：
10.1007/s10958-013-1375-9
中图分类号：
学科分类号：
摘要：
Parametric Painlevé equations are the ODEs for which general solutions can be represented in parametric form in terms of Painlevé functions. Most of these ODEs do not possess the Painlevé property. Considering similarity solutions of the Short Pulse Equation and its decoupled generalization, we derive a nontrivial example of a parametric Painlevé equation related to the third Painlevé equation. We also discuss some analytic properties of this equation describing the structure of movable singularities. Bibliography: 14 titles © 2013 Springer Science+Business Media New York.
引用
收藏
页码：81 / 90
页数：9
相关论文
共 50 条
  • [31] Painlevé Test and Higher Order Differential Equations
    Uğurhan Muğan
    Fahd Jrad
    Journal of Nonlinear Mathematical Physics, 2002, 9 : 282 - 310
  • [32] Solutions of the first and second Painlevé equations are meromorphic
    Aimo Hinkkanen
    Ilpo Laine
    Journal d’Analyse Mathématique, 1999, 79 : 345 - 377
  • [33] On Hamiltonian structures of quasi-Painlevé equations
    Filipuk, Galina
    Stokes, Alexander
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2023, 56 (49)
  • [34] Bilinear Equations on Painlevé τ Functions from CFT
    M. A. Bershtein
    A. I. Shchechkin
    Communications in Mathematical Physics, 2015, 339 : 1021 - 1061
  • [35] Parameterless discrete Painlevé equations and their Miura relations
    B. Grammaticos
    A. Ramani
    Journal of Nonlinear Mathematical Physics, 2016, 23 : 141 - 149
  • [36] Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies
    A. V. Domrin
    B. I. Suleimanov
    M. A. Shumkin
    Proceedings of the Steklov Institute of Mathematics, 2020, 311 : 98 - 113
  • [37] On properties of meromorphic solutions for difference Painlevé equations
    Chang-Wen Peng
    Zong-Xuan Chen
    Advances in Difference Equations, 2015
  • [38] Preface to Special Issue on the Geometry of the Painlevé equations
    Nalini Joshi
    Masatoshi Noumi
    Hidetaka Sakai
    Claude M. Viallet
    Journal of Nonlinear Mathematical Physics, 2013, 20 : 1 - 2
  • [39] Noncommutative Painlev, Equations and Systems of Calogero Type
    Bertola, M.
    Cafasso, M.
    Rubtsov, V.
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 363 (02) : 503 - 530
  • [40] Quadratic transformations for the third and fifth Painlevé equations
    Kitaev A.V.
    Journal of Mathematical Sciences, 2006, 136 (1) : 3586 - 3595
12345