Extended Prelle-Singer method and integrability/solvability of a class of nonlinear nth order ordinary differential equations

被引：24

作者：

Chandrasekar V.K. ^{[1
]}

Senthilvelan M. ^{[1
]}

Lakshmanan M. ^{[1
]}

机构：

[1] Centre for Nonlinear Dynamics, Bharathidasan University

来源：

Journal of Nonlinear Mathematical Physics | 2005年 / 12卷 / Suppl 1期

关键词：

D O I：

10.2991/jnmp.2005.12.s1.16

中图分类号：

学科分类号：

摘要：

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 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.

引用

页码：184 / 201

页数：17

共 18 条

[1] Lakshmanan M., Rajasekar S., Nonlinear Dynamics: Integrability Chaos and Patterns, (2003)
[2] Bruschi M., Calogero F., Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space I, J. Nonlinear Math. Phys., 7, pp. 303-385, (2000)
[3] Calogero F., A technique to identify solvable dynamical systems and another solvable extension of the goldfish many-body problem, J. Math. Phys., 45, pp. 4661-4678, (2004)
[4] Bruschi M., Calogero F., Integrable systems of quartic oscillators, Phys. Lett. A, 273, pp. 173-182, (2000)
[5] Prelle M., Singer M., Elementary first integrals of differential equations, Trans. Am. Math. Soc., 279, pp. 215-229, (1983)
[6] Duarte L.G.S., Duarte S.E.S., Da Mota A.G.P., Skea J.E.F., Solving the second-order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A, 34, pp. 3015-3024, (2001)
[7] Chandrasekar V.K., Senthilvelan M., Lakshmanan M., On the Complete Integrability and Linearization of Certain Second Order Nonlinear Ordinary Differential Equations
[8] Chandrasekar V.K., Senthilvelan M., Lakshmanan M., New aspects of integrability of force-free duffing-van der Pol oscillator and related nonlinear systems, J. Phys. A, 37, pp. 4527-4534, (2004)
[9] Chandrasekar V.K., Senthilvelan M., Lakshmanan M., An Unusual Liénard Type Nonlinear Oscillator with Properties of a Linear Harmonic Oscillator
[10] Chandrasekar V.K., Senthilvelan M., Lakshmanan M., A note on solving third order ordinary differential equations through the extended Prelle-Singer procedure, Proceedings of the Second National Conference on Nonlinear Systems and Dynamics, (2005)

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