3 edition of **Exact WKB analysis for the degenerate third Painleve equation of type (Ds)** found in the catalog.

Exact WKB analysis for the degenerate third Painleve equation of type (Ds)

Hideaki Wakako

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- 20 Currently reading

Published
**2007**
by Kyōto Daigaku Sūri Kaiseki Kenkyūjo in Kyoto, Japan
.

Written in English

**Edition Notes**

Statement | by Hideaki Wakako and Yoshitsugu Takei. |

Series | RIMS -- 1596 |

Contributions | Takei, Yoshitsugu., Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. |

Classifications | |
---|---|

LC Classifications | MLCSJ 2007/00046 (Q) |

The Physical Object | |

Pagination | 13 p. ; |

Number of Pages | 13 |

ID Numbers | |

Open Library | OL16508834M |

LC Control Number | 2008554982 |

The Painlevé equations are six families P I, P II, P III, P IV, P V, P VI of second order differential equations in [equation] of the form [equation] Author: Martin A. Guest, Claus Hertling. The fourth-order equation for description of nonlinear waves is considered. A few variants of this equation are studied. Painlevé test is applied to investigate integrability of these equations. We show that all these equations are not integrable, but some exact solutions of these equations by: 6.

Painlevé Differential Equations in the Complex Plane. Series:De Gruyter Studies in The third Painlevé equation (P3) Gromak, Valerii I. / Laine, Ilpo / Shimomura, Shun. 30,00 € / $ / £ Get Access to Full Text. Citation Information. Painlevé Differential Equations in the Complex Plane. Walter de Gruyter. Pages: The third Painlevé equation in generic form depends on two parameters m and n, and it has rational solutions if and only if at least one of the parameters is an integer. We use known algebraic representations of the solutions to study numerically how the distributions of poles and zeros behave as increases and how the patterns vary by: 2.

equation in question are parametrized. For each Painleve equation, this surface is characterized by´ a pair of a ne root systems which represent the symmetry type and the surface type. Many prop-erties of Painleve equations as presented in Section 2 are systematically controlled by geometry of´ the by: Exact WKB analysis for continuous and discrete Painlev´e equations — Stokes geometry, connection formula and wall-crossing formula Information. Date. Ap – Speaker. Yoshitsugu Takei (RIMS, Kyoto University) Video. Thematic Programs.

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Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type $(D_8)$ is discussed.

Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear by: 2.

Exact WKB analysis for instanton-type solutions of the degenerate third Painlev e equation of type (D8) is discussed. Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear equations.

1 Introduction In this paper we discuss the exact WKB analysis for instanton-type solutions (i.e. Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type (D8) is discussed.

Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear equations. Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type $(D_8)$ is discussed.

of type (D8) in the exact WKB analysis By YOShitSUgu Takei* Abstract In [W] and [TW] the exact WKB theoretic structure of the most degenerate third Painlevé equation of type (D8) was investigated. In this paper we announce a result that this degenerate third Painlevé equation of type (D8) plays a special role of the canonical equation near a simple pole of Painlevé equations.

Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type (D8) is discussed. Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear : Hideaki Wakako and Yoshitsugu Takei.

On the role of the degenerate third Painlevé equation of type (D8) Keyphrases exact wkb analysis degenerate third painlev equation. of exact WKB analysis. Since the work of Sakai [S] on geometrical classi cation of the space of initial conditions of Painlev e equations, it is considered to be natural to distinguish the degenerate third Painlev e equations of type (D7) and (D8) from the generic third Painlev e equation (PIII).

Several important properties such as ˝-functions, irreducibility etc. of these degenerate third Painlev e. Painleve analysis and exact solutions of two dimensional Korteweg-de Vries-Burgers equation M P JOY Materials Research Centre, Indian Institute of Science, BangaloreIndia MS received 5 April ; revised 26 September Abstract.

Two dimensional Korteweg-de Vries-Burgers equation is shown to be non-integr-able using Painleve Size: 1MB. The turning point problems for instanton-type solutions of Painlevé equations with a large parameter are discussed. Generalizing the main result of [4] near a simple turning point, we report in this paper that Painlevé equations can be transformed to the second Painlevé equation and the most degenerate third Painlevé equation near a double turning point and near a simple pole, : Yoshitsugu Takei.

Painlevé analysis. By extension, this denotes all the methods based on singularities, whose aim is to generate any kind of closed-form result (particular solution, ﬁrst integral, Darboux polynomial, Lax pair, etc). More in [5].

Classiﬁcations. This denotes the exhaustivelists of ODEs in a certain class (e.g. third order second. Whitham equation (FW), Some of these equations have shown to possess Painlevé property, therefore, are Painleve integrable while the rest did not pass the test and reasons for that are conjectured.

Keywords: Painlevé analysis method, The potential Boussinesq equation, The murrary equation. The degenerate third Painlevé equation, where and, is studied via the isomonodromy deformation method. Asymptotics of general regular and singular solutions as τ → ±∞ an.

_____: On the exact WKB analysis for the third order ordinary differential equations with a large parameter, Asian J. Math., 2 (), – zbMATH MathSciNet Google Scholar [AKT3] _____: On the exact steepest descent method: A new method for the description of Stokes curves, J.

Math. Phys., 42 (), – zbMATH CrossRef Cited by: 2. In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified.

Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation by: Abstract.

The Painlevé analysis introduced by Weiss, Tabor, and, Carnevale (WTC) in for nonlinear partial differential equations (PDEs) is an extension of the method initiated by Painlevé and Gambier at the beginning of this century for the classification of algebraic nonlinear differential equations (ODEs) without movable critical by: Most equations in their classification were reducible to a linear differential equation or solvable by elliptici functions, and only six equations eventually remained to be unreducible (or ``irreducible'') to classical special functions.

These six equations are now called the Painlevé equations. The six Painlevé equations (P I –P VI) were first discovered about a hundred years ago by Painlevé and his colleagues in an investigation of nonlinear second-order ordinary differential ly, there has been considerable interest in the Painlevé equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse by: We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painlevé III equation under a general point transformation.

Their sufficiency is established by reduction to known results for the equations of the form y″ = f(x, y). We consider separately the generic case and the case of reducibility to an autonomous by: 3.

In this paper we construct all Painlevé‐type differential equations of the form (d 2 y/dx 2) 2 = F(x,y,dy/dx), where F is rational in y and y′=dy/dx, locally analytic in x, and not a perfect further simplifying assumptions are made, but it is found that the absence of a term linear in y″ in the class of equations under investigation forces F to be a polynomial in y and y′.Cited by:.

Quasi-linear Stokes phenomenon for the Painlevé first equation. A A Kapaev. as well as the isomonodromy deformation approach based on the so-called exact WKB analysis, Takei has re-derived the latter result Painlevé equations, topological type property and reconstruction by the topological recursionCited by: PAINLEVE ANALYSIS FOR NONLINEAR PARTIAL´ DIFFERENTIAL EQUATIONS Micheline Musette Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2 B– Brussel Proceedings of the Carg`ese school (3–22 June ) La propri´et´e de Painlev´e, un si`ecle apr`es The Painlev´e property, one century later Size: KB.Painlevé Equations — Nonlinear Special Functions Peter A Clarkson School of Mathematics, Statistics and Actuarial Science University of Kent, Canterbury, CT2 7NF, UK [email protected] UK-Japan Winter School, “Nonlinear Analysis” Royal Academy of Engineering, London 7 January