title: Interconnections between various analytic approaches applicable to third-order nonlinear differential equations.
abstract: We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle-Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli, Tamilnadu 620 024, India.
authors.forename: R
authors.initials: R
authors.lastname: Mohanasubha
authors.affiliation: Centre for Nonlinear Science and Engineering , School of Electrical and Electronics Engineering, SASTRA University , Thanjavur, Tamilnadu 613 401, India.
authors.forename: V K
authors.initials: VK
authors.lastname: Chandrasekar
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli, Tamilnadu 620 024, India.
authors.forename: M
authors.initials: M
authors.lastname: Senthilvelan
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli, Tamilnadu 620 024, India.
authors.forename: M
authors.initials: M
authors.lastname: Lakshmanan
keywords: Darboux polynomials; Jacobi last multipliers; integrating factors; null forms; symmetries; third-order nonlinear differential equations