Three-dimensional Bessel light bullets in self-focusing Kerr media

We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schrodinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.