Nonlinear waves are particular solutions of partial differential equations which have a well-defined spatio-temporal structure. The focus of this talk is on multidimensional traveling waves which describe propagation phenomena with constant speed. We present an approach to the existence of such waves which relies upon methods from the theory of infinite-dimensional dynamical systems (center manifold reduction, normal form theory). During the last decades this approach led to significant progress in the understanding of nonlinear waves. In particular, it allowed to rigorously construct various types of multidimensional waves for different types of problems, as for instance, three-dimensional water-waves (doubly periodic waves, periodically modulated solitary waves), corner defects in interface propagation, or defects in periodic patterns (dislocations, grain boundaries).
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