Localized Airy Wave Packets in a Self-Defocusing Kerr Medium

Families of vortex-like and Gaussian-like localized Airy wave packets, propagating in a self-defocusing Kerr medium, are discovered. Their propagation is described by the cylindrical Korteweg-de Vries (CKdV) equation, reduced from the nonlinear Schrödinger equation by utilizing the reductive perturbation technique. The CKdV equation is solved using the Hirota bilinear method to obtain analytical Airy wave packet families of different order. In particular, we focus on the distribution of optical intensity via numerical simulations of the Airy wave packet solutions, obtained for different initial phases and amplitudes, at given propagation distances. In distinction to the usual ring solitons, the Airy wave packets display a novel internal structure, which reveals novel nonlinear phenomena during the propagation of packets.