In this paper we explore the effect of the generalized uncertainty principle and modified dispersion relation to compute Hawking radiation from a rotating acoustic black hole in the tunneling formalism by using the Wentzel-Kramers-Brillouin (WKB) approximation applied to the Hamilton-Jacobi method. The starting point is to consider the planar acoustic black hole metric found in a Lorentz-violating Abelian Higgs model. In our analyzes we investigate quantum corrections for the Hawking temperature and entropy. A logarithmic correction and an extra term that depends on a conserved charge were obtained. We also have found that the changing in the Hawking temperature ${cal T}_H$ for a dispersive medium due to a Lorentz-violating background accounts for supersonic velocities in the general form $(v_g-v_p)/v_p = Delta {cal T}_H/{cal T}_Hsim10^{-5}$ in Bose-Einstein-Condensate (BEC) systems.
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