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The fundamental mode of a CANDLE burn-up wave, propagating into fertile material, in one-dimensional geometry was derived analytically with the result that the fluence and the neutron flux shapes turned out to be a Gudermannian and a Secans Hyperbolicus, respectively, of a Galilean variable. Furthermore, the fundamental evolution equation for the neutron flux was represented and discussed thoroughly. All other higher dimensional cases, however, have to be treated by numerical methods.

The analytical representation of the fundamental mode in 1-D-geometry for the CANDLE burn-up phenomenon