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[en] We define a mapping of the QCD Balitsky-Kovchegov equation in the diffusive approximation with noise and a generalized coupling allowing a common treatment of the fixed and running QCD couplings. It corresponds to the extension of the stochastic Fisher and Kolmogorov-Petrovskii-Piscounov equation to the radial wave propagation in a medium with negative-gradient absorption responsible for anomalous diffusion, noninteger dimension, and damped noise fluctuations. We obtain its analytic traveling-wave solutions with a new scaling curve and for running coupling a new scaling variable allowing to extend the range and validity of the geometric-scaling QCD prediction beyond the previously known domain.