The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to ...The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to a slow modulation of the dominant pattern.Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation,which is called the Ginzburg-Landau(G-L for short) equation,for the amplitudes of the dominating modes.展开更多
基金supported by the Deanship of Scientific Research,University of Hail,KSA(No.0150258)
文摘The main goal of this paper is to approximate the Kuramoto-Shivashinsky(K-S for short) equation on an unbounded domain near a change of bifurcation,where a band of dominant pattern is changing stability.This leads to a slow modulation of the dominant pattern.Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation,which is called the Ginzburg-Landau(G-L for short) equation,for the amplitudes of the dominating modes.
