Pinning, capture and release of fronts by localised inhomogeneities
Travelling wave fronts can be found in many PDEs which are invariant under spatial translations. Inhomogeneities break the translation invariance, hence no travelling waves can persist. On the other hand, the inhomogeneity can sustain a stationary front solution, even if the system without a homogeneity can not sustain stationary fronts. The stationary front is called a pinned front. A related feature is a travelling front which gets halted by the inhomogeneity, this is the so-called capture of fronts. And finally, the opposite can happen: a pinned front can release a travelling wave or even a periodic family of travelling waves as depicted in the figure. These phenomena are investigated for a forced and damped sine-Gordon equation with a localised inhomogeneity. This PDE is a model for example for long Josephson junctions with localised magnetic impurities.


