The second Painlevé equation in a problem concerning nonlinear effects near caustics

DOI10.1007/BF02364570zbMath0834.34008MaRDI QIDQ1189605

B. I. Sulejmanov

Publication date: 27 September 1992

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

asymptoticsnonlinear Schrödinger equationcausticssecond Painlevé transcendent

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (4)

Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as \(|x|\to\infty\) ⋮ Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation ⋮ Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation

Cites Work

• Connection formulae for Painlevé V functions
• The arithmetic of probability distributions
• Nonlinear effects upon waves near caustics
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