On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems. The theorem is applied to the Gray-Scott-Klausmeier vegetation-water interaction model.