The basic reactor physics of a completely new nuclear fast fission reactor-the Soliton Reactor-is presented. In such a fast reactor, based either on the U/Pu-or the Th/U-233 fuel cycle, an auto-catalytically driven flux-wave, similar to a water wave on shallow water, propagates through initially fertile regions thus burning it up and producing power. Hence, a qualitatively new kind of harnessing nuclear fission energy may become possible: without transports of irradiated fuel elements, reprocessing and-according to Edward Teller-by co-location of the reactor itself and the subterranean final disposal site in a sand bed about 100 m underground. Combined with the idea of an "energy island" soliton reactors could form the basis for a practically inexhaustible source of hydrogen for a climate-neutral energy source.