Linearization of third-order ordinary differential equations by generalized Sundman transformations: the case

DOI10.1016/j.cnsns.2009.06.020zbMath1222.34003OpenAlexW1479999575MaRDI QIDQ720040

Warisa Nakpim, Sergey V. Meleshko

Publication date: 13 October 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2009.06.020

zbMATH Keywords

linearization problemgeneralized sundman transformationnonlinear third-order ordinary differential equation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (12)

Third-order ordinary differential equations equivalent to linear second-order ordinary differential equations via tangent transformations ⋮ New non-standard Lagrangians for the Liénard-type equations ⋮ Linearization of fifth-order ordinary differential equations by generalized Sundman transformations ⋮ On the connection of the quadratic Liénard equation with an equation for the elliptic functions ⋮ Linearization of two second-order ordinary differential equations via fiber preserving point transformations ⋮ Lie group approach for constructing all reciprocal transformations: The two‐dimensional stationary gas dynamics equations ⋮ On solutions of third and fourth-order time dependent Riccati equations and the generalized Chazy system ⋮ On connections of the Liénard equation with some equations of Painlevé-Gambier type ⋮ On first integrals of second-order ordinary differential equations ⋮ On the integrability of Liénard i-type equations via \(\lambda \)-symmetries and solvable structures ⋮ Linearizability of nonlinear third-order ordinary differential equations by using a generalized linearizing transformation ⋮ On the criteria for integrability of the Liénard equation

Cites Work

• The characterization of third order ordinary differential equations admitting a transitive fiber-preserving point symmetry group
• Linearisable third-order ordinary differential equations and generalised sundman transformations: the case \(X=0\)
• The geometry of the equation \(y=f(x,y,y',y)\)
• Methods for constructing exact solutions of partial differential equations. Mathematical and analytical techniques with applications to engineering
• On linearization of third-order ordinary differential equations
• Ordinary differential equations which linearize on differentiation
• Linearization of fourth-order ordinary differential equations by point transformations
• Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations
• Linearization under nonpoint transformations

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