Exact discretization of the Ermakov-Pinney equation

DOI10.1016/S0375-9601(99)00744-6zbMath0946.34015OpenAlexW2059496194MaRDI QIDQ1569421

Andrew N. W. Hone

Publication date: 3 July 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(99)00744-6

zbMATH Keywords

Schrödinger operatorsfinite-dimensional Hamiltonian systemsDarboux transformationBäcklund transformationErmakov-Pinney equationexact discretizationdiscrete Schwarzian

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Nonlinear supersymmetric (Darboux) covariance of the Ermakov-Milne-Pinney equation ⋮ Nonlinearity from linearity: the Ermakov-Pinney equation revisited ⋮ Discrete Crum's theorems and lattice KdV-type equations ⋮ Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations ⋮ Symmetry reductions of a \(2+1\) Lax pair ⋮ Reciprocal link for \(2+1\)-dimensional extensions of shallow water equations

Cites Work

• Integrable symplectic maps
• The Hénon-Heiles system revisited
• A discrete Pinney equation
• Lie-theoretical generalization and discretization of the Pinney equation
• A bilinear approach to discrete Miura transformations.
• The constraints of potentials and the finite-dimensional integrable systems
• On Bäcklund transformations for many-body systems
• Linear r-matrix algebra for classical separable systems
• Bäcklund transformations for many-body systems related to KdV
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

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