title: Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems.
abstract: In this work, we establish a connection between the extended Prelle-Singer procedure and other widely used analytical methods to identify integrable systems in the case ofnth-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to thenth-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations.
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli 620024, 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 613401, India.
authors.forename: V K
authors.initials: VK
authors.lastname: Chandrasekar
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli 620024, India.
authors.forename: M
authors.identifier: 0000-0002-9494-9668
authors.initials: M
authors.lastname: Senthilvelan
authors.affiliation: Centre for Nonlinear Dynamics , School of Physics, Bharathidasan University , Tiruchirappalli 620024, India.
authors.forename: M
authors.initials: M
authors.lastname: Lakshmanan
keywords: Darboux polynomials; Jacobi last multiplier; integrating factors; null forms; symmetries