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We consider dynamics of fluctuations in transonically acceleratingBose-Einstein condensates and luminous liquids (coherent light propagating in aKerr nonlinear medium) using the hydrodynamic approach. It is known thatneglecting the quantum potential (QP) leads to a singular behavior of quantumand classical fluctuations in the vicinity of the Mach (sonic) horizon, whichin turn gives rise to the Hawking radiation. The neglect of QP is well foundedat not too small distances $|x| \gg l_h$ from the horizon, where $l_h$ is thehealing length. Taking the QP into account we show that a second characteristiclength $l_r > l_h$ exists, such that the linear fluctuation modes becomeregularized for $|x| \ll l_r$. At $|x| \gg l_r$ the modes keep their singularbehavior, which however is influenced by the QP. As a result we find adeviation of the high frequency tail of the spectrum of Hawking radiation fromPlanck's black body radiation distribution. Similar results hold for the wavepropagation in Kerr nonlinear media where the length $l_h$ and $l_r$ exist dueto the nonlinearity.

Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation