  In uniaxial soft matter with a reorientational nonlinearity, such as nematic
liquid crystals, a light beam in the extraordinary polarization walks off its
wavevector due to birefringence, while it undergoes self-focusing via an
increase in refractive index and eventually forms a spatial soliton. Hereby the
trajectory evolution of solitons in nematic liquid crystals- nematicons- in the
presence of a linearly varying transverse orientation of the optic axis is
analysed. In this study we use and compare two approaches: i) a slowly varying
(adiabatic) approximation based on momentum conservation of the soliton in a
Hamiltonian sense; ii) the Frank-Oseen elastic theory coupled with a fully
vectorial and nonlinear beam propagation method. The models provide comparable
results in such a non-homogeneously oriented uniaxial medium and predict curved
soliton paths with either monotonic or non-monotonic curvatures. The minimal
power needed to excite a solitary wave via reorientation remains essentially
the same in both uniform and modulated cases.
