On the integrability conditions for a family of Liénard-type equations

DOI10.1134/S1560354716050063zbMath1355.34006arXiv1608.06920OpenAlexW3099499025MaRDI QIDQ2520097

Nikolay A. Kudryashov, Dmitry I. Sinelshchikov

Publication date: 13 December 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.06920

zbMATH Keywords

closed-form solutiongeneral solutionnonlocal transformationsLiénard-type equationPainlevé-Gambier equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

Integrable nonautonomous Liénard-type equations ⋮ Construction and study of exact solutions to a nonlinear heat equation ⋮ Optical dromions and domain walls with the Kundu-Mukherjee-Naskar equation by the Laplace-Adomian decomposition scheme ⋮ Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods ⋮ Exact solutions to a family of position‐dependent mass damped oscillators from variational λ‐symmetries ⋮ On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations ⋮ On the integrability of Liénard i-type equations via \(\lambda \)-symmetries and solvable structures ⋮ On the integrability of the Abel and of the extended Liénard equations ⋮ Systems of Vector Fields for the Integration of Ordinary Differential Equations ⋮ Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations ⋮ Self-similar solutions of the Burgers hierarchy ⋮ Nonlinear problems with blow-up solutions: numerical integration based on differential and nonlocal transformations, and differential constraints ⋮ An identity for the Heaviside function and its application in representation of nonlinear Green's function

Cites Work

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• On the criteria for integrability of the Liénard equation
• Lie point symmetries classification of the mixed Liénard-type equation
• On connections of the Liénard equation with some equations of Painlevé-Gambier type
• Linearization of second-order ordinary differential equations by generalized Sundman transformations
• Paul Painlevé and his contribution to science
• The dynamics of a body with an axisymmetric base sliding on a rough plane
• The dynamics of three vortex sources
• On the connection of the quadratic Liénard equation with an equation for the elliptic functions
• On the Jacobi last multiplier, integrating factors and the Lagrangian formulation of differential equations of the Painlevé-Gambier classification
• Dynamics and control of an omniwheel vehicle
• Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
• Exact travelling wave solutions of non-linear reaction-convection-diffusion equations—An Abel equation based approach
• The Jacobi Last Multiplier and its applications in mechanics
• On a unique nonlinear oscillator
• On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations
• Application of the Generalised Sundman Transformation to the Linearisation of Two Second-Order Ordinary Differential Equations

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