The Dynamics of Modulated Wave Trains (Memoirs of the American Mathematical Society)

Arjen Doelman; Bjorn Sandstede; Arnd Scheel; Guido Schneider

Editorial: American Mathematical Society, 2009
ISBN 10: 0821842935 / ISBN 13: 9780821842935
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Brand new. We distribute directly for the publisher. 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. N° de ref. de la librería

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Sinopsis: The authors of this title 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.

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Detalles bibliográficos

Título: The Dynamics of Modulated Wave Trains (...
Editorial: American Mathematical Society
Año de publicación: 2009
Encuadernación: Paperback
Condición del libro: New

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Arjen Doelman
Editorial: American Mathematical Society (2009)
ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción American Mathematical Society, 2009. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780821842935

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Arjen Doelman, Bjorn Sandstede, Arnd Scheel
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ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción American Mathematical Society, United States, 2009. Paperback. Estado de conservación: New. Language: English . Brand New Book. The authors of this title 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. Nº de ref. de la librería AAN9780821842935

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Arjen Doelman, Bjorn Sandstede, Arnd Scheel
Editorial: American Mathematical Society, United States (2009)
ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción American Mathematical Society, United States, 2009. Paperback. Estado de conservación: New. Language: English . Brand New Book. The authors of this title 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. Nº de ref. de la librería AAN9780821842935

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Doelman, Arjen/ Sandstede, Bjorn/ Scheel, Arnd/ Schneider, Guido
Editorial: Amer Mathematical Society (2009)
ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción Amer Mathematical Society, 2009. Paperback. Estado de conservación: Brand New. 105 pages. 9.84x6.69x0.24 inches. In Stock. Nº de ref. de la librería __0821842935

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Doelman, Arjen, Sandstede, Bjorn, Scheel, Arnd, Schneider, Guido
Editorial: Amer Mathematical Society (2009)
ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción Amer Mathematical Society, 2009. Estado de conservación: Very Good. Ships from the UK. Great condition for a used book! Minimal wear. Nº de ref. de la librería GRP97469891

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Arjen Doelman, Bjorn Sandstede, Arnd Scheel, Guido Schneider
Editorial: Amer Mathematical Society (2009)
ISBN 10: 0821842935 ISBN 13: 9780821842935
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Descripción Amer Mathematical Society, 2009. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0821842935

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