A method of identifying integrability quantifiers from an obvious λ-symmetry in second-order nonlinear ordinary differential equations. (November 2019)

• Record Type: Journal Article
• Authors: Mohanasubha, R.; Chandrasekar, V.K.; Senthilvelan, M.
• Is Part Of: International journal of non-linear mechanics. Volume 116(2019)
• Page Start: 318
• Page End: 323
• Publication Date: 2019-11
• Subjects: Nonlinear ordinary differential equations -- λ-symmetries -- Integrating factors -- Integrability; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.06.010
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this paper, we present an algorithm to derive second λ -symmetry vector field from the first λ -symmetry vector field for a class of second order nonlinear ordinary differential equations. We then employ the method introduced by Muriel et. al. (2017) and derive two independent integrals for a non-polynomial nonlinear oscillator equation. We also derive several integrability quantifiers for this equation with the help of the two λ - symmetries. Highlights: We propose a new way to find second λ -symmetry from first λ - symmetry vector field. Using two λ -functions along with two new functions, we can find two independent integrals. Several integrability quantifiers are identified with the help of four functions.