Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain

The mani goal of tills paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded dornaiti hear 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.