We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.
Kartashov, Y.V., Vysloukh, V.A., Torner, L. Highly-asymmetric soliton complexes in parabolic optical lattices. "Optics letters", Gener 2008, vol. 33, núm. 2, p. 141-143.