The basic reactor physics of a completely novel nuclear fission reactor design - the soliton-reactor - is presented on the basis of a simple model. In such a reactor, the neutrons in the critical region convert either fertile material in the adjacent layers into fissile material or reduce the poisoning of fissile material in such a manner that successively new critical regions emerge. The result is an autocatalytically driven burn-up wave which propagates throughout the reactor. Thereby, the relevant characteristic spatial distributions (neutron flux, specific power density and the associated particle densities) are solitons -wave phenomena resulting from non-linear partial differential equations which do not change their shape during propagation. A qualitatively new kind of harnessing nuclear fission energy may become possible with fuel residence times comparable with the useful lifetime of the reactor system. In the long run, fast breeder systems which exploit the natural uranium and thorium resources, without any reprocessing capacity are imaginable.