We report experimental results on the dynamics of excitation waves in a modified Belousov-Zhabotinsky reaction. The waves in this system obey nonmonotonic dispersion relations. This anomaly induces the stacking of excitation fronts into patterns with stable interpulse distances. The stacking process creates either a traveling shock structure or a cascade of bunching events in which metastable wave packets are formed. The direction and the speed of the shock are explained in terms of a simple

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... metrical analysis. We also present experimental evidence for the corresponding instabilities in two-dimensional systems. Here, wave stacking generates atypical structures in the collision of target patterns and wave bunching is accompanied by complex front deformations.