Chirped periodic and localized waves of the (1+2)-dimensional chiral nonlinear Schrödinger equation

Abstract

We study the existence and stability of nonlinearly chirped periodic waves and soliton structures in an optical medium wherein the pulse propagation is governed by the (1+2)-dimensional chiral nonlinear Schrödinger equation. An exact periodic wave solution is presented for the model equation in the presence of all physical processes by using the complex envelope traveling-wave ansatz. A class of optical gray-type solitons is obtained in the special long wave limit. The properties of these structures such as the velocity and wave number are determined by the system parameters. It is found that the frequency chirp accompanying these optical waves is inversely proportional to the intensity of the wave and its amplitude can be controlled by choosing the dispersion parameter appropriately. In addition, the stability of these waveforms is discussed numerically under some initial perturbations. The results show that those nonlinear waves can propagate in a stable fashion in the nonlinear medium under finite initial perturbations, such as amplitude and white noise.