Quick search Find article
Quick search
Find article

Existence and uniqueness of tri-tronquée solutions of the second Painlevé hierarchy

N Joshi1 and M Mazzocco2,3

Show affiliations


Recommended by P Deift

The first five classical Painlevé equations are known to have solutions described by divergent asymptotic power series near infinity. Here, we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlevé equation. Moreover, we prove that these are unique in certain sectors near infinity.


PACS

02.30.Gp Special functions

02.30.Hq Ordinary differential equations

MSC

33E17 Painlevé-type functions

34M30 Asymptotics, summation methods

34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Subjects

Mathematical physics

Dates

Issue 2 (March 2003)

Received 29 May 2002, in final form 1 November 2002

Published 18 December 2002



  1. Existence and uniqueness of tri-tronquée solutions of the second Painlevé hierarchy

    N Joshi and M Mazzocco 2003 Nonlinearity 16 427

  2. Laplace Transform of Spherical Bessel Functions

    A Ludu and R F O'Connell 2002 Phys. Scr. 65 369

  3. A modified adiabatic approach to positron-atom and positron-molecule polarisation potentials: application to positron-He scattering

    T L Gibson 1990 J. Phys. B: At. Mol. Opt. Phys. 23 767

  4. Localised polaronic states in mixed-valence linear chain complexes

    D Baeriswyl and A R Bishop 1988 J. Phys. C: Solid State Phys. 21 339

  5. Ferromagnetic resonance of ultrathin metallic layers

    Michael Farle 1998 Rep. Prog. Phys. 61 755

  6. Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams

    A van de Walle and M Asta 2002 Modelling Simul. Mater. Sci. Eng. 10 521

  7. MRA and low-separation rank approximation with applications to quantum electronics structures computations

    G I Fann et al 2005 J. Phys.: Conf. Ser. 16 461

  8. Dissipative particle dynamics with energy conservation

    J. Bonet Avalos and A. D. Mackie 1997 Europhys. Lett. 40 141

  9. Mesoscopic two-phase model for describing apparent slip in micro-channel flows

    R. Benzi et al 2006 Europhys. Lett. 74 651

  10. A maximum a posteriori reconstruction method for plasma tomography

    Natalia Denisova 2004 Plasma Sources Sci. Technol. 13 531

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Linear and nonlinear rogue wave statistics in the presence of random currents*
  2. Semiclassical analysis and passive imaging
  3. Theory of fields of extremals for multiple integrals
More

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.