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 with other widely used analytical methods to identify integrable systems in the case of $n^{th}$-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods we bring out the interlink between Lie point symmetries, contact symmetries, $\lambda$-symmetries, adjoint-symmetries, null forms, Darboux polynomials, integrating factors, Jacobi last multiplier and generalized $\lambda$-symmetries corresponding to the $n^{th}$-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.

25 pages, 1 figure, to appear in Proc. R. Soc. A

References in corpus (3)

• Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second order differential equations
• Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations
• Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

Cited by in corpus (1)

• A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations