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 ordinary differentiable equations (ODEs). We establish an important interconnection between 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.

Accepted for publication in Proceedings of the Royal Society of London A

References in corpus (2)

• Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second order differential equations
• On the linearization of isochronous centre of a modified Emden equation with linear external forcing

Cited by in corpus (3)

• Interplay of symmetries and other integrability quantifiers in finite dimensional integrable nonlinear dynamical systems
• Cosmological solutions in the Brans-Dicke theory via invariants of symmetry groups
• A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations