Spatiotemporal optical similaritons in dual-core waveguide with an external source

We explore analytically and numerically the existence of exact asymptotic spatiotemporal optical self-similar light bullets to the nonlinear Schrödinger equation with gain in the presence of an external source in (3+1)-dimensions. This model appertains to the description of self-similar wave propagation through asymmetric planar dual-core waveguide (DWG) amplifiers. The asymmetric DWG is composed of two adjoining, closely spaced, upper and lower waveguides, in which the lower one acts as a passive waveguide while the upper waveguide is an active one. Due to the linear coupling between them, we can control the dynamical behaviors of the wave propagating through the passive waveguide by controlling the wave in active waveguide. We explicate the mechanism to control the dynamical behaviors of these self-similar waves for two specific cases: (i) when the gain and width are hyperbolic functions and (ii) when the gain and width are periodic functions.