Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-08-28
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Proceedings of the Royal Society London Series A (Accepted for publication) 25 pages, one table
Scientific paper
10.1098/rspa.2005.1465
A method of 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. In addition to the above we introduce a novel way of deriving linearizing transformations from the first integrals to linearize the second order nonlinear ordinary differential equations to free particle equation. We illustrate the theory with several potentially important examples and show that our procedure is widely applicable.
Chandrasekar V. K.
Lakshmanan Meenakshi
Senthilvelan M.
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