  We show that the stability condition for the soliton-like wave of nuclear
burning in neutron-multiplicating 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
(fissile) 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 ststistics of the Gaussian
simplectic ensembles with respect to the parameter that describes the squared
width of burning wave front of nuclear fuel active component.
