Abstract
In this paper we present a new type of combined solitary wave solution for the variable coefficients higher-order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity, which governs the propagation of optical pulses in the heterogeneous optical fiber system under certain parametric conditions. Unlike those previously-reported solitary wave solutions for the classes HNLS, the expression of this solution in this paper is a composition of the summation of a hyperbolic secant function and a hyperbolic tangent function, and the solution can show the properties of bright and dark soliton respectively. Furthermore, we investigate the stability of the combined solitary wave solution under the small perturbation of noise, amplitude and phase position by using numerical simulation method.
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