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Physical fundamentals of traveling wave reactor are considered. We show that the condition of existence of nuclear burning soliton-like wave in a neutron-multiplying medium is determined in general by two conditions. The first condition (necessary) is determined by relationship between the equilibrium concentration and critical concentration of active (fissionable) isotope that is a consequence of the Bohr–Sommerfeld quantization condition. The second condition (sufficient) is set by the so-called Wigner quantum statistics, or more accurately, by a statistics of the Gaussian simplectic ensembles with respect to the parameter that describes the squared width of burning wave front of nuclear fuel active component

Traveling Wave Reactor and Condition of Existence of Nuclear Burning Soliton-Like Wave in Neutron-Multiplying Media