  We investigate the properties of a real scalar field in the Finslerian
Randers spacetime, where the local Lorentz violation is driven by a geometrical
background vector. We propose a dynamics for the scalar field by a minimal
coupling of the scalar field and the Finsler metric. The coupling is
intrinsically defined on the Randers spacetime, and it leads to a non-canonical
kinetic term for the scalar field. The nonlinear dynamics can be split into a
linear and nonlinear regimes, which depend perturbatively on the even and odd
powers of the Lorentz-violating parameter, respectively. We analyze the
plane-waves solutions and the modified dispersion relations, and it turns out
that the spectrum is free of tachyons up to second-order.
