Numerical studies of the fourth Painlevé equation

DOI10.1093/imamat/50.2.167zbMath0782.65099OpenAlexW2093002795MaRDI QIDQ4202149

Peter A. Clarkson, Andrew P. Bassom, Andrew C. Hicks

Publication date: 31 August 1993

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imamat/50.2.167

zbMATH Keywords

Schrödinger equationasymptotic behaviourfourth Painlevé equationinverse scatteringsoliton equationnumerical investigation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (14)

Addendum: Painlevé transcendents and PT -symmetric Hamiltonians (2015 J. Phys. A: Math. Theor. 48 475202) ⋮ Rigorous analytical approximation of tritronquée solution to Painlevé-I and the first singularity ⋮ A dynamical systems approach to the fourth Painlevé equation ⋮ Asymptotic behavior of the fourth Painlevé transcendents in the space of initial values ⋮ Design of evolutionary cubic spline intelligent solver for nonlinear Painlevé-I transcendent ⋮ New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations ⋮ Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation ⋮ Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant ⋮ New exact solutions of the discrete fourth Painlevé equation ⋮ On integrable Ermakov-Painlevé IV systems ⋮ Painlevé IV with both Parameters Zero: A Numerical Study ⋮ Application of fuzzy Picard method for solving fuzzy quadratic Riccati and fuzzy Painlevé I equations ⋮ Painlevé IV: A numerical study of the fundamental domain and beyond ⋮ Nonclassical symmetry reductions of the Boussinesq equation

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