Dynamics of self-similar waves in asymmetric twin-core fibers with Airy–Bessel modulated nonlinearity

We explore the exact optical similaritons of a generalized nonlinear Schrödinger equation (GNLSE) with space–time modulated dispersion, nonlinearity, external potential and inhomogeneous source. It is shown here that this equation appertains to the description of wave propagation through asymmetric twin-core fibers in which we control the dynamics of the pulse propagating through passive fiber by controlling the dynamics of the self-similar wave propagating through the active fiber, due to the linear coupling between them. By utilizing multivariate similarity transformation, we map the nonautonomous GNLSE to standard NLSE with a homogeneous external source. Furthermore, by using Möbius transformation, we find periodic waves, solitary waves, and pure cnoidal and pure snoidal solutions as exact solutions. As an application, we explicate the mechanism to control the dynamical behaviors of these similaritons for a spatial Airy and Bessel modulated nonlinearity.