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

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

2005-01-25

arxiv.org/abs/nlin/0501045v1

J. Non. Math. Phys. Vol. 12, Sub. 1, 184 - 201, (2005)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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.

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