Dynamical behavior and traveling wave solutions in optical fibers with Schrödinger–Hirota equation

Abstract

This paper mainly focuses on bifurcation and dispersive soliton solutions in optical fibers with Schrödinger–Hirota equation. By using the traveling wave transformation, the Schrödinger–Hirota equation is reduced to two-dimensional dynamical system, which is analyzed in detail by the theory of planar dynamical systems. We obtain a series of new solutions, which include periodic wave solutions, bell solitary wave solutions and kink solitary wave solutions. Then some other traveling wave solutions of Schrödinger–Hirota equation are constructed via the complete discriminant system method. In particular, it is notable that these solutions may help us to explore new phenomena of the Schrödinger–Hirota equation in nonlinear optics. The obtained solutions substantially improve the corresponding results in the known literatures.