Optical Solitary Wave Solutions for the Fourth-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Abstract

We present several kinds of optical solitary wave solutions for the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation describing the propagation of optical pulses in a medium that exhibits a parabolic nonlinearity law. Among them, apart from some regular fundamental bright solitary wave solutions and dark solitary wave solutions given, there are also two kinds of combined solitary wave solutions, i.e., bright and dark solitary wave and W-shaped solitary wave solutions which describe bright and dark solitary wave properties. It is found that their amplitude may approach nonzero when the time variable approaches infinity. Moreover, when the parameters of the bright and dark solitary wave are selected appropriately, the kink and anti-kink solitary wave solutions, which are first reported in the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, are discovered.

New Exact Solutions of (1 + 1)-Dimensional Coupled Integrable Dispersionless System

“…From Fig. 2, the arch-basin soliton, which is similar to W-shaped soliton in virtue of the higher nonlinear effects in nonlinear optics, [28] evolves into dark soliton, and finally annihilates. From Figs.…”

High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions

“…In the present paper, the dispersive cubic-quintic Schrödinger equation (DCQSE) including higher-order time derivatives is studied through the exp a -function scheme. The nonlinear governing model in its dimensionless form is presented as below [25][26][27]:…”

“…Some recent research works related to the model (1) are listed here. Dai et al [25] employed the generalized projected Riccati expansion method to acquire a wide range of new exact solutions to the model (1). The solitary wave solutions of the model (1) were also gained by Azzouzzi and her colleagues [26] by means of the complex envelope function approach.…”

Domain wall arrays, fronts, and bright and dark solitons in a generalized derivative nonlinear Schrödinger equation

“…In the last three decades, great progress has been made on the construction of exact solutions of NLSE. Many significant methods for NLSE have been established, such as the inverse scattering method [1], Darboux transformation [2], Hirota bilinear method [3], F-expansion method [4], the generalized projected Ricatti equation expansion method [5], Jacobian elliptic function expansion method [6], the tanh function expansion method [7], the similarity transformation method [8], etc.…”