  The influence of a Lorentz-violation on soliton solutions generated by a
system of two coupled scalar fields is investigated. Lorentz violation is
induced by a fixed tensor coefficient that couples the two fields. The
Bogomol'nyi method is applied and first-order differential equations are
obtained whose solutions minimize energy and are also solutions of the
equations of motion. The analysis of the solutions in phase space shows how the
stability is modified with the Lorentz violation. It is shown explicitly that
the solutions preserve linear stability despite the presence of Lorentz
violation. Considering Lorentz violation as a small perturbation, an analytical
method is employed to yield analytical solutions.
