THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
From MaRDI portal
Publication:3754924
DOI10.1080/16073606.1985.9631915zbMath0618.34009OpenAlexW1979461488WikidataQ115295144 ScholiaQ115295144MaRDI QIDQ3754924
F. M. Mahomed, Peter G. L. Leach
Publication date: 1985
Published in: Quaestiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/16073606.1985.9631915
Nonlinear ordinary differential equations and systems (34A34) Applications of Lie groups to the sciences; explicit representations (22E70)
Related Items
Real Forms of the Complex Twisted N=2 Supersymmetric Toda Chain Hierarchy in Real N=1 and Twisted N=2 Superspaces ⋮ Hidden symmetries and linearization of the modified Painlevé–Ince equation ⋮ A group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=. I. Equations having nonmaximal number of Lie point symmetries ⋮ Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view ⋮ Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry ⋮ Symmetry and singularity properties of second-order ordinary differential equations of Lie's Type III. ⋮ Autonomous self-similar ordinary differential equations and the Painlevé connection ⋮ Classification of a modified de Sitter metric by variational symmetries and conservation laws ⋮ Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains ⋮ On first integrals, conservation laws and reduction of classes of Emden and Liénard equations ⋮ Linearizability criteria for systems of two second-order differential equations by complex methods ⋮ Algebraic properties of first integrals for scalar linear third-order ODEs of maximal symmetry ⋮ Algebraic linearization criteria for systems of ordinary differential equations ⋮ Lie and Riccati linearization of a class of Liénard type equations ⋮ Symmetry classification of first integrals for scalar linearizable second-order ODEs ⋮ Lie point symmetries for systems of second order linear ordinary differential equations ⋮ USE OF LIE SYMMETRIES AND THE PAINLEVÉ ANALYSIS IN COSMOLOGY ⋮ Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra ⋮ A systematic analysis of the properties of the generalised Painlevé-Ince equation ⋮ Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems ⋮ On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations ⋮ Unnamed Item ⋮ Symmetries, integrals and solutions of ordinary differential equations of maximal symmetry ⋮ First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation ⋮ On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations ⋮ Ordinary differential equations invariant under translation in the independent variable and rescaling: The Lagrangian formulation ⋮ Singularity analysis of a variant of the Painlevé-Ince equation ⋮ Exact solution of a thin film flow of an Oldroyd 6-constant fluid over a moving belt ⋮ Complete symmetry groups of ordinary differential equations and their integrals: Some basic considerations ⋮ Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation ⋮ Nonlinear ordinary differential equations: A discussion on symmetries and singularities ⋮ Noether symmetries and the quantization of a Liénard-type nonlinear oscillator ⋮ Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations ⋮ THE LIE ALGEBRA sl(3, R) AND LINEARIZATION ⋮ Invariant Linearization Criteria for Systems of Cubically Nonlinear Second-Order Ordinary Differential Equations ⋮ Exceptional properties of second and third order ordinary differential equations of maximal symmetry ⋮ Symmetries of first integrals and their associated differential equations ⋮ Dynamics of the Painlevé-Ince equation ⋮ Symmetry, singularities, and integrability in complex dynamics. II: Rescaling and time-translation in two-dimensional systems ⋮ Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability ⋮ Invertible point transformations, Painlevé test, and the second Painlevé transcendent
Cites Work
- Unnamed Item
- A generalization of Lie's 'counting' theorem for second-order ordinary differential equations
- Similarity methods for differential equations
- Noether's theory in classical nonconservative mechanics
- The complete symmetry group of a forced harmonic oscillator
- Symmetries of the time-dependent N-dimensional oscillator
- On the Lie symmetries of the classical Kepler problem
- An exact invariant for a class of time-dependent anharmonic oscillators with cubic anharmonicity
- Generalizations of Noether’s Theorem in Classical Mechanics
- Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
- The Lie group of Newton's and Lagrange's equations for the harmonic oscillator
- Symmetry groups and conserved quantities for the harmonic oscillator
- Three-Dimensional Isotropic Harmonic Oscillator and SU3
- On the Problem of Degeneracy in Quantum Mechanics