A note on the application of Darboux polynomial method to an nonlinear oscillator equation. (October 2019)

• Record Type: Journal Article
• Authors: Mohanasubha, R.; Senthilvelan, M.
• Is Part Of: International journal of non-linear mechanics. Volume 115(2019)
• Page Start: 49
• Page End: 52
• Publication Date: 2019-10
• Subjects: Darboux polynomials -- First integrals -- Liénard type equations; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.04.012
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this paper, we apply Darboux polynomial method to a second-order nonlinear ordinary differential equation x ̈ + ( k 1 x q + k 2 ) x ̇ + k 3 x 2 q + 1 + k 4 x q + 1 + λ x = 0 . We identify several integrable cases in this model. We report Darboux polynomials, exponential factor and first integral for seven different choices of parameters that appear in this model. Several well known polynomial oscillator equations come out as a sub-class of the obtained results.