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

DOI

10.2991/jnmp.2005.12.s1.16How to use a DOI?

Abstract

We discuss a method of solving nth order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordnary 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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V.K. Chandrasekar
AU  - M. Senthilvelan
AU  - M. Laksmanan
PY  - 2005
DA  - 2005/01/01
TI  - Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear nth Order Ordinary Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 184
EP  - 201
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.16
DO  - 10.2991/jnmp.2005.12.s1.16
ID  - Chandrasekar2005
ER  -