Bifurcations and dispersive optical solitons for the nonlinear Schrödinger–Hirota equation in DWDM networks

Abstract

The main purpose of this paper is to study the dynamical behaviors and optical solitons in DWDM networks with Schrödinger–Hirota equation. First of all, the Schrödinger–Hirota equation was converted into plane dynamical system by using the traveling wave transform and some other suitable transform, which has been analyzed in detail via the theory of bifurcations for dynamical system. As we can see, a range of new soliton solutions are obtained. Then, with the assistance of the complete discriminant system method and symbolic computation, some other optical soliton solutions are constructed, which include Jacobi elliptic function solutions, hyperbolic function solutions, rational function solutions, solitary wave solutions and trigonometric function solutions. In particular, it is worth noting that these optical soliton solutions may motivate us to explore new phenomena which may appear in this equation. Finally, two-dimensional and three-dimensional graphs are drawn by selecting some specific parameters.