Login | Register

On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation


On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation

Bertola, Marco (2012) On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation. Nonlinearity, 25 (4). pp. 1179-1185. ISSN 0951-7715

Text (application/pdf)
bertola2012.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1088/0951-7715/25/4/1179


Using a simple operator-norm estimate we show that the solution to the second Painlevé equation within the Ablowitz–Segur family is pole-free in a well-defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Authors:Bertola, Marco
Journal or Publication:Nonlinearity
Digital Object Identifier (DOI):10.1088/0951-7715/25/4/1179
ID Code:976932
Deposited On:05 Mar 2013 15:52
Last Modified:18 Jan 2018 17:43


[1] Ablowitz M J and Fokas A S 2003 Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics) 2nd edn (Cambridge: Cambridge University Press)

[2] Bertola M and Cafasso M 2011 The transition between the gap probabilities from the Pearcey to the Airy process—a Riemann–Hilbert approach Int. Math. Res. Not. at press

[3] Dubrovin B, Grava T and Klein C 2009 On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the tritronquée solution to the Painlevé-I equation J. Nonlinear Sci. 19 57–94

[4] Fokas A S and Zhou X 1992 On the solvability of Painlevé II and IV Commun. Math. Phys. 144 601–22

[5] Fokas A S, Its A R, Kapaev A A and Novokshenov V Yu 2006 Painlevé Transcendents (Mathematical Surveys and Monographs vol 128) (Providence, RI: American Mathematical Society)

[6] Hastings S P and McLeod J B 1980 A boundary value problem associated with the second Painlevé transcendent and the Korteweg–de Vries equation Arch. Ration. Mech. Anal. 73 31–51

[7] Its A R and Kapaev A A 2002 The Nonlinear Steepest Descent Approach to the Asymptotics of the Second Painlevé Transcendent in the Complex Domain (Progress in Mathematical Physics vol 23) (Boston, MA: Birkhäuser Boston)

[8] Its A R, Izergin A G, Korepin V E and Slavnov N A 1990 Differential equations for quantum correlation functions Proc. Conf. on Yang–Baxter Equations, Conformal Invariance and Integrability in Statistical Mechanics and Field Theory Internat. J. Modern Phys. B 4 1003–37

[9] Kapaev A A 2004 Quasi-linear Stokes phenomenon for the Painlevé first equation J. Phys. A: Math. Gen. 37 11149–67

[10] Masoero D 2010 Poles of integrále tritronquée and anharmonic oscillators. A WKB approach J. Phys. A: Math. Theor. 43 095201

[11] Novokshenov V Yu 2009 Padé approximations for Painlevé I and II transcendents Teoret. Mat. Fiz. 159 515–26 (in Russian) Novokshenov V Yu 2009 Theoret. Mat. Phys. 159 853–62 (Engl. transl.)

[12] Segur H and Ablowitz M J 1981 Asymptotic solutions of nonlinear evolution equations and a painlevé transcedent Physica. D 3 165–84

[13] Tracy C A and Widom H 1994 Level-spacing distributions and the Airy kernel Commun. Math. Phys. 159 151–74
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top