Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2005-10-17
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Submitted to Proceedings of the Royal Society London Series A, 21 pages
Scientific paper
10.1098/rspa.2005.1648
We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given equation so that the general solution follows straightforwardly from these integrals. The method is illustrated with several examples. Further, we propose a powerful method of identifying linearizing transformations. The proposed method not only unifies all the known linearizing transformations systematically but also introduces a new and generalized linearizing transformation (GLT). In addition to the above, we provide an algorithm to invert the nonlocal linearizing transformation. Through this procedure the general solution for the original nonlinear equation can be obtained from the solution of the linear ordinary differential equation.
Chandrasekar V. K.
Lakshmanan Meenakshi
Senthilvelan M.
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