The Dynamics of Modulated Wave Trains is popular PDF and ePub book, written by A. Doelman in 2009, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Dynamics of Modulated Wave Trains can be Read Online from any device for your convenience.
The Dynamics of Modulated Wave Trains Book PDF Summary
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.
Detail Book of The Dynamics of Modulated Wave Trains PDF
- Author : A. Doelman
- Release : 21 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821842935
- Genre : Mathematics
- Total Page : 122 pages
- Language : English
- PDF File Size : 15,6 Mb
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