Complex optical solutions and modulation instability of hyperbolic Schrödinger dynamical equation

Abstract

Complex hyperbolic Schrödinger equation describes ultra-short pulse propagation in nonlinear media fiber optics. In this paper, new complex solutions for the complex hyperbolic Schrödinger equation are constructed using generalized elliptic equation rational expansion method. The aquired new solutions are complex rational, trigonometric and hyperbolic solution expressed by kink solitons, bright solitons, singular solitons and periodic solutions. The moment of obtained solutions are graphically illustrated to show the physical properties of this model. Such types of models arising in physics and nonlinear sciences can also be solved by this reliable, powerful and effective method. The conditions for the stability of obtained results are also discussed using modulation instability analysis.