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A.S. Landsberg and E. Knobloch. 1993. New Types of Waves in Systems with O(2) Symmetry. Physics Letters A 179: 316.

A number of novel phenomena arising in systems with O(2) symmetry are described. These include pulsing traveling waves with either a periodically or quasiperiodically modulated phase velocity, and heteroclinic waves which alter their appearance with time, taking successively the form of pure traveling waves, standing waves and steady states. Chaotic waves can also be present. These states result from the codimension-two interaction between a reflection-breaking steady state bifurcation and a reflection-preserving Hopf bifurcation from a circle of nontrivial equilibria. The resulting waveforms are illustrated using a model of magnetoconvection with periodic boundary conditions.

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