Kink properties in Lorentz-violating scalar field theory

We consider topological defects for the $\lambda\phi^4$ theory in (1+1) dimensions with a Lorentz-violating background. It has been shown, by M. Barreto et al. (2006) \cite{barreto2006defect}, one cannot have original effects in (the leading order of) single scalar field model. Here, we introduce a new Lorentz-violating term, next to leading order which cannot be absorbed by any redefinition of the scalar field or coordinates. Our term is the lowest order term which leads to concrete effects on the kink properties. We calculate the corrections to the kink shape and the corresponding mass. Quantization of the kink is performed and the revised modes are obtained. We find the bound and continuum states are affected due to this Lorentz symmetry violation.