In a quasi-one-dimensional reaction-diffusion-migration system based on the methylene blue-sulfide-oxygen oscillatory reaction in a matrix of polyacrylamide gel, almost stationary patterns are observed. A weak electrical field applied to the system induces waves which travel toward the cathode. Close to the anode, the initially observed stationary pattern remains stable. In some experiments, a lateral instability of the wave front is also observed. The spatio-temporal dynamics is analyzed by the Karhunen-Loeve decomposition technique, and entropy-like quantities are used to describe the dynamics. Numerical simulations based on a chemically realistic model confirm the experimental observations.