Self-similar evolutions of trigonometric and Hermite-Gaussian optical pulses in asymmetric twin-core fibers

We analytically explore two novel types of asymptotic self-similar solutions, termed trigonometric and Hermite-Gaussian pulses of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, gain or absorption, and external source. Under certain physical conditions, we reduce the coupled nonlinear Schrödinger equations to a single-wave equation that aptly describes similariton propagation through asymmetric twin-core fiber amplifiers.