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Improvement of Harmonic Balance Using Jacobian Elliptic Functions

Journal of Applied Mathematics and Physics 2015年第6期3卷 680-690页

作者： Serge Bruno Yamgoué Bonaventure Nana olivier tiokeng lekeufack Department of Physics Higher Teacher Training College-Bambili The University of Bamenda Bamenda Cameroon Laboratory of Mechanics Department of Physics Faculty of Science The University of Yaoundé 1 Yaoundé Cameroon

We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.

关键词： Harmonic Balance Linearization Continuous Force Function Single Degree-of-Freedom Conservative System Jacobian Elliptic Functions Symmetric Oscillations

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Signature of chaos in the semi quantum behavior of a classically regular triple well heterostructure

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Natural Science 2010年第3期2卷 145-154页

作者： tiokeng olivier lekeufack Serge Bruno Yamgoue Timoleon Crepin Kofane 不详

We analyze the phenomenon of semiquantum chaos in the classically regular triple well model from classical to quantum. His dynamics is very rich because it provides areas of regular be-havior, chaotic ones and multiple quantum tun-neling depending on the energy of the system as the Planck’s constant varies from 0 to 1. The Time Dependent Variational Principle TDVP using generalized Gaussian trial wave function, which, in many-body theory leads to the Hartree Fock Approximation TDHF, is added to the tech-niques of Gaussian effective potentials and both are used to study the system. The extended classical system with fluctuation variables non- linearly coupled to the average variables exhibit energy dependent transitions between regular behavior and semi quantum chaos monitored by bifurcation diagram together with some numerical indicators.

关键词： Nonlinear Dynamics Semi Quantum Chaos Effective Potential

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