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I consider a class of one-dimensional models where Majorana fermions interactwith bosonic fields. Contrary to a more familiar situation where bosonicdegrees of freedom are phonons and as such form a slow subsystem, I considerfast bosons. Such situation exists when the bosonic modes appear as collectiveexcitations of interacting electrons as, for instance, in superconductors orcarbon nanotubes. It is shown that an entire new class of excitations emerge,namely bound states of solitons and Majorana fermions. The latter bound statesare not topological and their existence and number depend on the interactionsand the soliton's velocity. Intriguingly the number of bound states increaseswith the soliton's velocity.

Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields