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Asymptotic Methods in the Theory of Nonlinear Oscillations
TLDR
In this article, a wide circle of engineering-technical and scientific workers who are concerned with oscillatory processes is devoted to the approximate asymptotic methods of solving the problems in the theory of nonlinear oscillations met in many fields of physics and engineering.Abstract:
: This book is devoted to the approximate asymptotic methods of solving the problems in the theory of nonlinear oscillations met in many fields of physics and engineering. It is intended for the wide circle of engineering-technical and scientific workers who are concerned with oscillatory processes. Contents include the following: Natural oscillations in quasi-linear systems; The method of the phase plane; The influence of external periodic forces; The method of the mean; Justification of the asymptotic methods.read more
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A universal instability of many-dimensional oscillator systems
TL;DR: In this article, the authors demonstrate the mechanism for a universal instability, the Arnold diffusion, which occurs in the oscillating systems having more than two degrees of freedom, which results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations.
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Some asymptotic methods for strongly nonlinear equations
TL;DR: In this paper, a survey of recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones, is presented.
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The world of the complex Ginzburg-Landau equation
Igor S. Aranson,Lorenz Kramer +1 more
TL;DR: The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community as mentioned in this paper, it describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity, and Bose-Einstein condensation to liquid crystals and strings in field theory.
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Generalized averaging method for power conversion circuits
TL;DR: In this paper, a more general averaging procedure that encompasses state-space averaging and that is potentially applicable to a much broader class of circuits and systems is presented, including resonant type converters.
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Notes on the homotopy analysis method: Some definitions and theorems
TL;DR: In this article, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers, are described.