Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear $n$th Order Ordinary Differential Equations

Abstract

We discuss a method of solving $n^{th}$ order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordinary differential equations. We also introduce a novel way of generating additional integrals of motion from a single integral. We illustrate the theory for both second and third order equations with suitable examples. Further, we extend the method to two coupled second order equations and apply the theory to two-dimensional Kepler problem and deduce the constants of motion including Runge-Lenz integral.

18 pages, Article dedicated to Professor F. Calogero on his 70thbirthday

Cited by in corpus (6)

• Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability
• A Simple and Unified Approach to Identify Integrable Nonlinear Oscillators and Systems
• Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
• 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