  This paper shows a new approach to obtain analytical topological defects of a
2D Myers-Pospelov Lagrangian for two scalar fields. Such a Lagrangian presents
higher-order kinetic terms, which lead us to equations of motion which are
non-trivial to be integrated. Here we describe three possible scenarios for the
equations of motion, named by timelike, spacelike and lightlike respectively.
We started our investigation with a kink-like travelling wave Ansatz for the
free theory, which led us to constraints for the dispersion relations of each
scenario. We also introduced a procedure to obtain analytical solutions for the
general theory in the three mentioned scenarios. We exemplified the procedure
and discussed the behavior of the defect solutions carefully. It is remarkable
that the methodology presented in this study led to analytical models, despite
the complexity of the equations of motion derived from the 2D Myers-Pospelov
Lagrangian. The methodology here tailored can be applied to several Lagrangians
with higher-order derivative terms.
