Classical Lagrangians for momentum dependent Lorentz violation

Certain momentum-dependent terms in the fermion sector of the Lorentz-violating standard model extension (SME) yield solvable classical Lagrangians of a type not mentioned in the literature. These cases yield new relatively simple examples of Finsler and pseudo-Finsler structures. One of the cases involves antisymmetric $d$-type terms and yields a new example of a relatively simple covariant Lagrangian.