On the links between some generalized Pinney and nonlinear Gambier equations

DOI10.1006/jmaa.1999.6321zbMath0933.34097OpenAlexW2086960065MaRDI QIDQ1301886

Micheline Musette

Publication date: 12 September 1999

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6321

zbMATH Keywords

Painlevé propertysecond-order nonlinear differential equationsgeneralized Pinney and nonlinear Gambier equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Cites Work

• Lie-theoretical generalization and discretization of the Pinney equation
• Nonlinear evolution equations, rescalings, model PDES and their integrability: I
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Nonlinear interaction of traveling waves of nonintegrable equations
• Bäcklund transformation of partial differential equations from the Painlevé–Gambier classification. I. Kaup–Kupershmidt equation
• Comments on the Eckhaus PDE iψ _t +ψ _xx +2(∣ψ∣ ² ) _x ψ+∣ψ∣ ⁴ ψ=0
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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