Self-similar spatiotemporal solitary waves in Bessel–Hermite optical lattices

An exact self-similar solution to a (3+1)-dimensional nonlinear Schrödinger equation with gain in the Bessel-Hermite lattice is obtained analytically. The stability of the analytical solution is confirmed by using numerical simulation. It is shown that the light bullet has a stable ellipsoid or vortex profile and a linear spatiotemporal chirp.