Symmetric and asymmetric solitons in two-dimensional dual-core waveguides with a one-dimensional lattice

We introduce a model for spatiotemporal solitons in a symmetric system of parallel linearly coupled planar optical waveguides carrying a transverse grating. It also applies to the description of two-dimensional matter-wave solitons in parallel two-dimensional diskâ€"shaped traps combined with a one-dimensional optical lattice. Using the variational approximation and numerical methods, we demonstrate that attenuation of the linear coupling between the cores causes reduction in the stable part of the family of symmetric solitons. Eventually, this family detaches from the asymmetric one and becomes entirely unstable. Close to the symmetry-breaking bifurcation (SBB), unstable symmetric solitons evolve into asymmetric quasisolitons, being destroyed far from the bifurcation. Unlike previously studied models, in the present setting the SBB is of the backward type, giving rise to an unstable branch of asymmetric solitons. Near the bifurcation, they transform into robust breathers.