scholarly journals Correction for Chandrasekar et al. , On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations

2008 ◽  
Vol 464 (2100) ◽  
pp. 3377-3377
Author(s):  
V. K. Chandrasekar ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Related Article ◽  
Link Type ◽  
Article Type

Correction for ‘On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations’ by V. K. Chandrasekar, M. Senthilvelan and M. Lakshmanan (Proc. R. Soc. A 461 , 2451–2476. (doi: 10.1098/rspa.2005.1465 )). The sentence preceeding equation (4.48) is incorrect and should read as follows.

scholarly journals On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations

2005 ◽  
Vol 461 (2060) ◽  
pp. 2451-2477 ◽  
Author(s):  
V.K Chandrasekar ◽  
M Senthilvelan ◽  
M Lakshmanan
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Free Particle ◽  
First Integrals ◽  
Second Order ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Integrals Of Motion ◽  
Integrating Factors

A method for finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle–Singer (PS) method is briefly discussed. We explore integrating factors, integrals of motion and the general solution associated with several dynamical systems discussed in the current literature by employing our modifications and extensions of the PS method. We also introduce a novel way of deriving linearizing transformations from the first integrals to linearize the second-order nonlinear ordinary differential equations to free particle equations. We illustrate the theory with several potentially important examples and show that our procedure is widely applicable.

scholarly journals On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations

2009 ◽  
Vol 465 (2108) ◽  
pp. 2369-2389 ◽  
Author(s):  
V. K. Chandrasekar ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Straightforward Method ◽  
The Given ◽  
Second Order Equations

Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe a simple and straightforward method to derive linearizing transformations for a class of two coupled SNODEs. Our procedure gives several new types of linearizing transformations of both invertible and non-invertible kinds. In both cases, we provide algorithms to derive the general solution of the given SNODE. We illustrate the theory with potentially important examples.

scholarly journals Oscillation criteria for second order differential equations with damping

1990 ◽  
Vol 49 (1) ◽  
pp. 43-54 ◽  
Author(s):  
S. R. Grace
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Linear Differential

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

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