  In order to characterize the common feature of the general Lorentz violation
models that the local speed of light is variable at ultrahigh energy scale, we
introduced a parameter n to characterize the variation of the speed of light
between inertial systems. And in order not to violate some fundamental
principles and experiments' results, some constraints were imposed on n. Then a
coordinate transformation with the parameter n, which meets the symmetry of
inertial systems, was naturally obtained. But just to satisfy the symmetry of
inertial systems, the expression for n cannot be determined. Inspired by the
idea of DSR model, we then discussed a specific expression for n that makes the
particle's energy have a limit rather than be infinite derived from the Lorentz
model. We found that the modified dispersion relation corresponding to the
specific expression for n is deeply associated with the general formula of
dispersion relation from the DSR. The motivation of introducing such a
parameter n was also discussed. Finally, we discussed the possible LIV effects
from astrophysical observations in GRB events and photon annihilation events.
Using the data from GRB 190114C we investigated the special dispersion relation
obtained in this paper and found that it appears to fit these data better than
the two models corresponding to the first or second order approximation of the
general formula of dispersion relation. And similar to the other Lorentz
violation models corresponding to the subluminal case, the modified dispersion
relation obtained in this paper can also result in increasing the energy
threshold of photon annihilation reaction, which is expected to be verified by
the future energetic photons events.
