  Some solutions to the anomalies of ultra high energy cosmic-ray(UHECR) and
TeV $\gamma$-rays require disturbed non-quadratic dispersion relations, which
suggest the Lorentz violation. Also, some new theories such as quantum gravity,
string theory and the standard model extension imply the Lorentz violation. In
this paper, we derive some transformation laws for the classical parameters of
nonlinear field system, and then provide their dispersion relations. These
dispersion relations also have non-quadratic form but keep the Lorentz
invariance. The analysis of this paper may be helpful for understanding the
quantum theory and the plausible Lorentz violation.
