Resurgence relations for classes of differential and difference equations

@article{Braaksma2004ResurgenceRF,
  title={Resurgence relations for classes of differential and difference equations},
  author={B. L. J. Braaksma and Robert Kuik},
  journal={Annales de la Facult{\'e} des Sciences de Toulouse},
  year={2004},
  volume={13},
  pages={479-492}
}
  • B. BraaksmaR. Kuik
  • Published 2004
  • Mathematics
  • Annales de la Faculté des Sciences de Toulouse
On considere, dans le contexte meromorphe, des equations differentielles et des equations aux differences de niveau 1. On peut representer les petites solutions de ces equations par des series exponentielles ou les coefficients sont des sommes de Borel de certaines series formelles. On considere la transition de Stokes dans ces representations quand les sommes de Borel des coefficients changent d'un secteur a un autre. On derive des relations de resurgence pour les coefficients dans ces series… 

On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations

We study a family of singularly perturbed linear partial differential equations with irregular type in the complex domain. In a previous work, Malek (2012), we have given sufficient conditions under

Tronquée Solutions of the Painlevé Equation PI

We analyze the one-parameter family of tronquée solutions of the Painlevé equation PI in the pole-free sectors together with the region of the first array of poles. We find a convergent expansion for

Tronquée Solutions of the Painlevé Equation PI

We analyze the one-parameter family of tronquée solutions of the Painlevé equation PI in the pole-free sectors together with the region of the first array of poles. We find a convergent expansion for

Computation of the Stokes Multipliers of Okubo's Confluent Hypergeometric System

The Stokes multipliers of Okubo’s confluent hypergeometric system can, in general, not be expressed in closed form using known special functions. Instead they may themselves be regarded as highly

Resurgence of the Euler-MacLaurin summation formula

The Euler-MacLaurin summation formula compares the sum of a function over the lattice points of an interval with its corresponding integral, plus a remainder term. The remainder term has an

Construction of solutions of nonlinear irregular singular differential equations by Borel summable functions and an application to Painlev\'{e} equations

A system of nonlinear differential equations x 1+ γ dYdx = F 0 ( x ) + A ( x ) Y + F ( x, Y ) is considered. The origin x = 0 is irregular singular. There exist pioneering works about them. We study

Resurgence and the Large $N$ Expansion

of the Dissertation Resurgence and the Large N Expansion by Ricardo Nuno Melo de Carmo Vaz Doctor of Philosophy in Physics Stony Brook University 2015 In this dissertation we focus on recent

On Inner Expansions for a Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities

A nonlinear singularly perturbed Cauchy problem with confluent Fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value

Dingle’s final main rule, Berry’s transition, and Howls’ conjecture

  • G. Nemes
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
The Stokes phenomenon is the apparent discontinuous change in the form of the asymptotic expansion of a function across certain rays in the complex plane, known as Stokes lines, as additional

References

SHOWING 1-10 OF 10 REFERENCES

Transseries for a class of nonlinear difference equations

Given a nonlinear analytic difference equation of level 1 with a formal power series solution ŷ 0 we associate with it a stable manifold of solutions with asymptotic expansion ŷ 0. This manifold can

Transseries in difference and differential equations

In dit proefschrift worden niet-lineaire stelsels van differentiaal- en differentievergelijkingen bestudeerd in een omgeving van het punt ∞ in het complexe vlak C. ... Zie: Samnvatting

) form a complete and free system of holomorphic invariants for (A) (invariance for analytic changes of the variables which do not change the formal normal form)

    Candelpergher (B.), Nosmas (J.-C.), Pham (F.)

    • Duke Math. J.,
    • 1993

    From the bridge equation (4.6) we may derive 039403B8 via (4.2) and then

      KUIK (R.). -Asymptotics and singularities for a class of difference equation

      • Contemporary Mathematics
      • 2004

      1 == ej,g = 0 and De = 039403C9, so G03B8(x,C) = exp