A computational overview of the solution space of the imaginary Painlevé II equation

DOI10.1016/j.physd.2015.07.008zbMath1364.34127OpenAlexW1008498141MaRDI QIDQ2396216

Bengt Fornberg, J. A. C. Weideman

Publication date: 7 June 2017

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2015.07.008

zbMATH Keywords

pole field solverTronquée solutionsAblowitz-Segur solutionsimaginary Painlevé IImodified Painlevé II

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (6)

Open problems for Painlevé equations ⋮ A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation ⋮ Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces ⋮ Asymptotic expansions relating to the distribution of the length of longest increasing subsequences ⋮ On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation ⋮ Connection formulas for the Ablowitz–Segur solutions of the inhomogeneous Painlevé II equation

Uses Software

• DLMF

Cites Work

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• Tronquée solutions of the Painlevé II equation
• A computational exploration of the second Painlevé equation
• A numerical methodology for the Painlevé equations
• Composite asymptotic expansions
• The isomonodromic deformation method in the theory of Painlevé equations
• Pure imaginary solutions of the second Painlevé equation
• Connection formulae for Painlevé functions
• Painlevé IV: A numerical study of the fundamental domain and beyond
• On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation
• Asymptotic Solutions of the Korteweg-deVries Equation
• On the asymptotic analysis of the Painleve equations via the isomonodromy method
• A new integration algorithm for ordinary differential equations based on continued fraction approximations
• Painlevé IV with both Parameters Zero: A Numerical Study

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