Lie-theoretical generalization and discretization of the Pinney equation
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Publication:1378695
DOI10.1006/jmaa.1997.5674zbMath0910.34013OpenAlexW2074500712MaRDI QIDQ1378695
Wolfgang K. Schief, Pavel Winternitz, Colin Rogers
Publication date: 19 April 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.1997.5674
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Structure theory for Lie algebras and superalgebras (17B05) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Lie algebras of linear algebraic groups (17B45)
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Cites Work
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- Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras
- The soliton correlation matrix and the reduction problem for integrable systems
- Systems of ordinary differential equations with nonlinear superposition principles
- The finite elastodynamics of hyperelastic thin tubes
- A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
- Bäcklund transformations and their applications
- A discrete Pinney equation
- Multi-component Ermakov systems: Structure and linearization
- Discretizing families of linearizable equations.
- Exact solution to the problem of forced large amplitude radial oscillations of a thin hyperelastic tube
- Primitive actions and maximal subgroups of Lie groups
- Group theoretical analysis of a rotating shallow liquid in a rigid container
- Superposition principles for matrix Riccati equations
- Classification of systems of nonlinear ordinary differential equations with superposition principles
- Superposition laws for solutions of differential matrix Riccati equations arising in control theory
- Superposition formulas for rectangular matrix Riccati equations
- Nonlinear evolution equations, rescalings, model PDES and their integrability: I
- Ermakov systems of arbitrary order and dimension: structure and linearization
- The Pinney equation and its discretization
- Superposition formulas for pseudounitary matrix Riccati equations
- Classification of the Finite Nonlinear Primitive Lie Algebras
- An algebraic model of transitive differential geometry
- The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0