Can I read The Dynamics of Modulated Wave Trains on EtoBox?

The Dynamics of Modulated Wave Trains by Arjen Doelman; Björn Sandstede; Arnd Scheel; Guido Schneider is a book available to read on EtoBox.

What is The Dynamics of Modulated Wave Trains about?

<p>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, fo

Author

Arjen Doelman; Björn Sandstede; Arnd Scheel; Guido Schneider

Publisher

Providence, R.I.: American Mathematical Society

Published

2009

Language

EN

ISBN

9780821842935

Subjects

Mathematics, Stem