Novel bright and kink similariton solutions of cubic-quintic nonlinear Schrödinger equation with distributed coefficients

Abstract

With the aid of the hidden symmetry reduction method, we derive two types of novel bright similariton solutions and one type of novel kink similariton solution for the cubic-quintic nonlinear Schrödinger equation with distributed coefficients. It is found that the existence conditions and properties of these similaritons are significantly different from those reported in previous literatures. Due to the introduction of three free parameters P, Q and R, the existence conditions of these similaritons are relaxed, which implies that there are more possibilities of the existence of similaritons in real inhomogeneous fibers. Moreover, the amplitude, center position and frequency shift of these similaritons can be regulated at will by choosing the free parameters Q, R, the gain/loss, linear external potential and dispersion parameters. As examples, the compression and periodic oscillation transmission of similaritons are presented in an exponential periodic system. The presented results enrich the transmission theory of similaritons in inhomogeneous optical fiber systems, and provide a valuable reference for the control of similaritons.