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Author: A. Doelman
Publisher: American Mathematical Soc.
ISBN: 0821842935
Category : Mathematics
Languages : en
Pages : 122
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Book Description
The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
Author: A. Doelman
Publisher: American Mathematical Soc.
ISBN: 0821842935
Category : Mathematics
Languages : en
Pages : 122
Get Book Here
Book Description
The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
Author: Arjen Doelman
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author:
Publisher: American Mathematical Soc.
ISBN: 0821866753
Category : Mathematics
Languages : en
Pages : 123
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Book Description
Author: J. Skourup
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
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Author: 江文山
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Author: Lev A. Ostrovsky
Publisher: Johns Hopkins University Press
ISBN: 9780801873256
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Waves occur naturally in a vast number of scientific or engineering situations. Ripples on a pond, the light we see, and the oscillations of bridges and buildings can often be described as solitary or interacting waves. Wave theory is therefore one of the most important branches of pure and applied science. In Modulated Waves: Theory and Applications Lev Ostrovsky and Alexander Potapov consider linear and nonlinear waves such as solitons, waves in inhomogeneous media, and many others. They discuss modulated waves—those characterized by a slow variation of the macroscopic parameters of amplitude, frequency, and profile. Most of the fundamentals of wave theory may be understood by considering this class of waves. Theoretical analysis is supported by examples from different branches of physics: electrodynamics, fluid mechanics, acoustics, optics, and the mechanics of solids.
Author: Wolfgang Dreyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
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Author: J. M. Arnold
Publisher:
ISBN:
Category :
Languages : en
Pages : 4
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The recent advances in the technology of passive optical amplification have brought closer the realisation of optical fibre communication systems using soliton pulses which are not limited by dispersion. This in turn creates a new generation of theoretical problems concerned with the evolution of information-bearing pulse trains along a nonlinear channel.
Author: Mårten Landahl
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Author: Marcello A. Faraco de Medeiros
Publisher:
ISBN:
Category :
Languages : en
Pages :
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