Modulating fronts in pattern-forming systems with oscillatory instabilityOnline: attendMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Pattern-forming systems with broken reflection symmetry $x \mapsto -x$ often exhibit periodic wavetrains with non-zero phase velocity, which bifurcate from a spatially homogeneous state as a bifurcation parameter increases. This type of instability is referred to as a Turing-Hopf or oscillatory instability and it can be found for example in a flow down a heated, inclined plane. In experiments, one observes that these periodic patterns typically arise in the wake of an invading heteroclinic front, which invades the unstable homogeneous state. Mathematically, this behavior can be modelled with a modulating traveling front solution, a traveling front connecting a periodic wavetrain to a spatially homogeneous state. I will present recent existence results for such solutions in a prototypical model with broken reflection symmetry.