Soliton catastrophes

We study the catastrophes that can occur in kink dynamics in the presence of external forces and impurities. Under the action of some anharmonic forces it can occur that not only the translational mode is unstable but also the internal modes (shape modes) or even part of the continuum spectrum (the soliton is unstable against the interaction with phonons). All this leads to interesting phenomena like soliton explosions. The length scale competition between the ''width'' of the inhomogeneities, the distance between them and the ''width'' of the kink leads to unexpected bifurcation phenomena. (author). 17 refs, 4 figs