Atlantis Press Paper Details: Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear nth Order Ordinary Differential Equations

title:

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

publication:

JNMP

volume-issue:

12 - Supplement 1

pages:

184 - 201

ISSN:

1402-9251

DOI:

doi:10.2991/jnmp.2005.12.s1.16 (how to use a DOI)

author(s):

V K CHANDRASEKAR, M SENTHILVELAN, M LAKSHMANAN

publication date:

January 2005

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.

© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.

full text:

12s1_16.pdf (172 K)

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title:		Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear nth Order Ordinary Differential Equations
publication:		JNMP
volume-issue:		12 - Supplement 1
pages:		184 - 201
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.s1.16 (how to use a DOI)
author(s):		V K CHANDRASEKAR, M SENTHILVELAN, M LAKSHMANAN
publication date:		January 2005
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:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		12s1_16.pdf (172 K)