Spatiotemporal self-similar waves for the (3 + 1)-dimensional inhomogeneous cubic–quintic nonlinear medium

Abstract

Spatiotemporal self-similar waves of the (3+1)-dimensional generalized nonlinear Schrödinger equation, describing propagation of optical pulses in a cubic–quintic nonlinear medium with inhomogeneous dispersion and gain, are derived. A one-to-one correspondence between such self-similar waves and solutions of the constant-coefficient cubic–quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss dynamical behaviors of self-similar waves in dispersion decreasing fiber.