On the complete integrability and linearization of nonlinear ordinary differential equations - Part IV: Coupled second order equations - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




On the complete integrability and linearization of nonlinear ordinary differential equations - Part IV: Coupled second order equations - Nonlinear Sciences > Exactly Solvable and Integrable Systems - Download this document for free, or read online. Document in PDF available to download.

Abstract: Coupled second order nonlinear differential equations are of fundamentalimportance in dynamics. In this part of our study on the integrability andlinearization of nonlinear ordinary differential equations we focus ourattention on the method of deriving general solution of two coupled secondorder nonlinear ordinary differential equations through the extendedPrelle-Singer procedure. We describe a procedure to obtain integrating factorsand required number of integrals of motion so that the general solution followsstraightforwardly from these integrals. Our method tackles both isotropic andnon-isotropic cases in a systematic way. In addition to the above, we introducea new method of transforming coupled second order nonlinear ODEs into uncoupledones. We illustrate the theory with potentially important examples.



Author: V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan

Source: https://arxiv.org/







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