1,721,016 research outputs found
The Elliptic Representation of the General Painlevé VI Equation
No full textIn this paper we study the analytic properties of elliptic representation of the general sixth Painlevé equation.
This is the first study in the literature
Trascendenti di Painlevé e integrabilità
Full text linkIn questo scritto verrà analizzato come sia possibile definire nuove funzioni speciali attraverso la soluzione di equazioni diffe- renziali e sviluppare metodi per conoscerne le proprietà di interesse, quando le equazio- ni stesse godono della così detta proprietà di Painlevé. In particolare, introdurremo le sei equazioni di Painlevé. Cioò permette di stabilire una nozione di integrabilità che si differenzia da quella nota in meccanica clas- sica (riduzione delle equazioni del moto a delle integrazioni), e che è molto importan- te per diversi modelli della fisica matematica contemporanea
The Elliptic Representation of the Painleve’ 6 Equation
No full textWe find a class of solutions of the sixth Painlevé equation corresponding to almost all the monodromy data of the associated linear system; actually, all data but one point in the space of data. We describe the critical behavior close to the critical points by means of the elliptic representation, and we find the relation among the parameters at the different critical points (connection problem)
Matching Procedure for the Sixth Painleve’ Equation
No full textIn the framework of the isomonodromy deformation method, we present
a constructive procedure to obtain the critical behaviour of Painlev´e VI
transcendents and solve the connection problem. This procedure yields
two- and one-parameter families of solutions, including trigonometric and
logarithmic behaviours, and three classes of solutions with Taylor expansion at
a critical point
Inverse Problem for Semisimple Frobenius Manifolds Monodromy Data and the Painlevé VI Equation
No full textThe singularity of Kontsevich's solution for QH*(CP2)
No full textIn this paper we study the nature of the singularity of the Kontsevich’s solution of the
WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two
coordinates systems of the Frobenius manifold given by the quantum cohomology of CP
A Review of the Sixth Painlevé Equation
No full textFor the Painleve' 6 transcendents, we provide a unitary description of the critical behaviours, the connection formulae, their complete tabulation, and the asymptotic distribution of poles close to a critical poin
On the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painleve’ 6 Equation
No full textIn this paper we find a class of solutions of the sixth Painlevé equation appearing in
the theory of WDVV equations. This class covers almost all the monodromy data associated to
the equation, except one point in the space of the data. We describe the critical behavior close to
the critical points in terms of two parameters and we find the relation among the parameters at
the different critical points (connection problem). We also study the critical behavior of Painlevé
transcendents in the elliptic representation
Solving the sixth painlevé equation: Towards the classification of all the ritical behaviors and the connection formulae
No full textThe critical behavior of a three real parameter class of solutions of the sixth Painlev´e
equation is computed, and parametrized in terms of monodromy data of the associated
2 × 2 matrix linear Fuchsian system of ODE. The class may contain solutions with poles
accumulating at the critical point. The study of this class closes a gap in the description
of the transcendents in an one to one correspondence with the monodromy data. These
transcendents are reviewed in the paper. Some formulas that relate the monodromy data
to the critical behaviors of the four real (two complex) parameter class of solutions
are missing in the literature, so they are computed here. A computational procedure
to write the full expansion of the four and three real parameter class of solutions is
proposed
Inverse Problem and Monodromy Data for 3-dimensional Frobenius Manifolds
No full textWe study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we
explicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI
transcendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric
form to explicitly construct polynomial and algebraic solutions and to derive the generating
function of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective
space. The procedure is a relevant application of the theory of isomonodromic deformation
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