On the application of solutions of the fourth Painlevé equation to various physically motivated nonlinear partial differential equations

zbMath0845.34006MaRDI QIDQ1907684

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

Publication date: 11 September 1996

Published in: Advances in Differential Equations (Search for Journal in Brave)

zbMATH Keywords

integrable systemsexact solutionsfourth Painlevé equationpotential nonlinear Schrödinger, spherical Boussinesq and \(2+ 1\)-dimensional dispersive long wave equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear ordinary differential equations and systems (34A34) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Explicit solutions, first integrals of ordinary differential equations (34A05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (4)

Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena ⋮ On integrable Ermakov-Painlevé IV systems ⋮ Painlevé IV: A numerical study of the fundamental domain and beyond ⋮ Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method

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