On the connection of the quadratic Liénard equation with an equation for the elliptic functions

DOI10.1134/S1560354715040073zbMath1383.34003OpenAlexW1092378824MaRDI QIDQ892769

Dmitry I. Sinelshchikov, Nikolay A. Kudryashov

Publication date: 12 November 2015

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

Full work available at URL: https://doi.org/10.1134/s1560354715040073

zbMATH Keywords

general solutionelliptic functionsnonlocal transformationsquadratic Liénard equation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Elliptic functions and integrals (33E05)

Related Items (14)

New non-standard Lagrangians for the Liénard-type equations ⋮ A functional realization of 𝔰𝔩(3, ℝ) providing minimal Vessiot–Guldberg–Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras ⋮ On some canonical classes of cubic-quintic nonlinear Schrödinger equations ⋮ Solitary and periodic waves in two-fluid magnetohydrodynamics ⋮ Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods ⋮ On deformations of classical mechanics due to Planck-scale physics ⋮ On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations ⋮ On connections of the Liénard equation with some equations of Painlevé-Gambier type ⋮ Exact solutions of the nonlinear diffusion equation ⋮ Nonlinear dynamics of a bubble contrast agent oscillating near an elastic wall ⋮ On the integrability conditions for a family of Liénard-type equations ⋮ Nonstandard Hamiltonian structures of the Liénard equation and contact geometry ⋮ Kudryashov and Sinelshchikov's method for solving the radial oscillation problem of multielectron bubbles in liquid helium ⋮ On the criteria for integrability of the Liénard equation

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