Periodic (higher-order) solitons are presumed to be a by-product of integrability and thus, in optics, applicable only to one-dimensional beams, propagating in a Kerr (cubic) nonlinear medium. Here, their existence is demonstrated numerically both in one and two transverse dimensions, propagating in a medium that differs radically from a Kerr nonlinearity. Our motivation comes from linear physics. This also provides physical understanding of higher-order solitons.

• Received 6 September 1994

DOI:https://doi.org/10.1103/PhysRevE.51.6297