Stable Hermite-Gaussian solitons in optical lattices

We report a family of solitons generated by Hermite-Gaussian beams that are supported in optical lattices, also described by Hermite-Gaussian functions in combination with a harmonic potential that is modelled by a (1+1)D nonlinear Schrodinger equation. We find that this kind of solitons is stable during propagation, provided they remain below a level of the power threshold. The pure local nonlinear system studied here can mimic, up to a certain extent, a strongly nonlocal medium, thus allowing generation of accessible solitons. These Hermite-Gaussian profiles constitute a kind of uncommon analytical solitons that allow the study of nonlinear wave behavior phenomena in a more tractable and closed form.