Algebraic linearization criteria for systems of ordinary differential equations

DOI10.1007/s11071-011-0128-xzbMath1251.34053OpenAlexW2051473441MaRDI QIDQ437339

Masood Khan, F. M. Mahomed, Muhammad Ayub

Publication date: 17 July 2012

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-011-0128-x

zbMATH Keywords

system of ODEsfour-dimentional Lie algebraslinearization by point transformation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14)

Related Items

Linearizing systems of second-order ODEs via symmetry generators spanning a simple subalgebra, Equality of the algebraic and geometric ranks of Cartan subalgebras and applications to linearization of a system of ordinary differential equations, Linearization: geometric, complex, and conditional, Symmetries of second-order systems of ODEs and integrability, On the algorithmic linearizability of nonlinear ordinary differential equations, Algebraic properties of first integrals for systems of second-order ordinary differential equations of maximal symmetry

Cites Work

• Unnamed Item
• The characterization of third order ordinary differential equations admitting a transitive fiber-preserving point symmetry group
• Linearization criteria for a system of second-order quadratically semi-linear ordinary differential equations
• Conditional linearizability criteria for a system of third-order ordinary differential equations
• Linearization of second order ordinary differential equations via Cartan's equivalence method
• Symmetry breaking for a system of two linear second-order ordinary differential equations
• Linearisable third-order ordinary differential equations and generalised sundman transformations: the case \(X=0\)
• The geometry of the equation \(y=f(x,y,y',y)\)
• Geometric proof of Lie's linearization theorem
• Symmetry Lie algebras of \(n\)th order ordinary differential equations
• Canonical forms for systems of two second-order ordinary differential equations
• Linearization criteria for a system of two second-order ordinary differential equations
• On linearization of third-order ordinary differential equations
• The relationship between the symmetries of and the existence of conserved vectors for the equation r^..+f(r)L+g(r)r=0
• Linearization of fourth-order ordinary differential equations by point transformations
• First integrals for a general linear system of two second-order ODEs via a partial Lagrangian
• Invariant Linearization Criteria for Systems of Cubically Nonlinear Second-Order Ordinary Differential Equations
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• Lie point symmetries for systems of second order linear ordinary differential equations
• Symmetries of the time-dependent N-dimensional oscillator
• Realizations of real low-dimensional Lie algebras
• Symmetries of Hamiltonian systems with two degrees of freedom
• THE LIE ALGEBRA sl(3, R) AND LINEARIZATION
• Symmetry group classification of ordinary differential equations: Survey of some results