Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-08-07
Nonlinear Sciences
Exactly Solvable and Integrable Systems
minor revision in section 2 and added a new reference. Proc. R. Soc. London A (accepted)
Scientific paper
10.1098/rspa.2008.0240
Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the method of deriving general solution of two coupled second order nonlinear ordinary differential equations through the extended Prelle-Singer procedure. We describe a procedure to obtain integrating factors and required number of integrals of motion so that the general solution follows straightforwardly from these integrals. Our method tackles both isotropic and non-isotropic cases in a systematic way. In addition to the above, we introduce a new method of transforming coupled second order nonlinear ODEs into uncoupled ones. We illustrate the theory with potentially important examples.
Chandrasekar V. K.
Lakshmanan Meenakshi
Senthilvelan M.
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