Amplitude Equation for Lattice Maps, a Renormalization Group Approach
P. Collet
Abstract
We consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps. Under some generic hypothesis we derive an amplitude equation which is the space-time continuous Ginzburg-Landau equation. Using dynamical renormalization group methods we control the accuracy of this approximation in a large ball of its basin of attraction.
Create a lesson
Related papers
Pulse Shepherding and Multi-Channel Soliton Transmission in Bit-Parallel-Wavelength Optical Fiber Links
Yuri S. Kivshar, Elena A. Ostrovskaya
A Particle Model of Rolling Grain Ripples Under Waves
K. H. Andersen
Two-color multistep cascading and parametric soliton-induced waveguides
Yuri S. Kivshar, Andrey A. Sukhorukov, Solomon M. Saltiel
Pattern formation in inclined layer convection
Karen E. Daniels, Eberhard Bodenschatz
On the Properties of Two Pulses Propagating Simultaneously in Different Dispersion Regimes in a Nonlinear Planar Waveguide
Monika E. Pietrzyk
Formation and Pinch-off of Viscous Droplets in the Absence of Surface Tension: an Exact Result
Mark Mineev-Weinstein, Gary D. Doolen, John E. Pearson et al.