Invariant manifold theory and modulation equations – the pursuit of reducing the complexity of mathematical models

Center manifold reduction and the derivation of amplitude and modulation equations are techniques which allow to replace complicated models by simpler equations that are more amenable to analysis and numerics. This talk illustrates the general spirit of these methods along several different examples whose common ground is the goal of understanding the dynamics of localized structures (such as fronts, pulses or wave packet) in nonlinear partial differential equations.