We introduce multipole soliton complexes in optical lattices induced bynondiffracting parabolic beams. Despite the symmetry-breaking dictated by thecurvature of the lattice channels, we find that complex, asymmetrichigher-order states can be stable. The unique topology of parabolic latticesaffords new types of soliton motion: single solitons launched into the latticewith nonzero transverse momentum perform periodic oscillations along parabolicpaths.
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