A class of solvable coupled nonlinear oscillators with amplitude independent frequencies |
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Authors: | VK Chandrasekar Jane H Sheeba R Gladwin Pradeep RS Divyasree M Lakshmanan |
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Institution: | 1. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India;2. Department of Physics, Amrita University, Kollam 690 525, Kerala, India |
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Abstract: | Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically. |
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Keywords: | Nonlinear oscillators Coupled ordinary differential equations Complete integrability Isochronous systems |
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