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On the nonlocal symmetries of certain nonlinear oscillators and their general solution. (English) Zbl 1250.34030
Summary: In this Letter we establish the integrability of two nonlinear oscillators {it through group theoretical method. We utilize the algorithm given in [{\it M.L. Gandarias} and {\it M.S. Bruzon}, J. Nonlinear Math. Phys. 18, No. supp01, 123-133 (2011)] and construct nonlocal symmetries for these two oscillators. From the knowledge of the latter we derive first integral and general solution for these two nonlinear nonpolynomial oscillator equations.
34C15Nonlinear oscillations, coupled oscillators (ODE)
37J35Completely integrable systems, topological structure of phase space, integration methods
Full Text: DOI
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