Wen-Rui Shan

Conservation laws and solitons for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Under investigation in this paper are the coupled cubic–quintic nonlinear Schrodinger equations describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media. Lax pair of the equations is obtained via the Ablowitz–Kaup–Newell–Segur scheme and the corresponding Darboux transformation is constructed. One-, two- and three-soliton solutions are presented and an infinite number of conservation laws are also derived. The features of solitons are graphically discussed: (i) head-on and overtaking elastic collisions of the two solitons; (ii) periodic attraction and repulsion of the bounded states of two solitons; (iii) energy-exchanging collisions of the three solitons.

Soliton collision in a general coupled nonlinear Schrödinger system via symbolic computation

A general coupled nonlinear Schrodinger system with the self-phase modulation, cross-phase modulation and four-wave mixing terms is investigated. The system is still integrable with the variable coefficients. Through the Hirota bilinear method, one- and two-soliton solutions are derived via symbolic computation. With the asymptotic analysis, it is found that the two-soliton solutions admit the inelastic and elastic collisions depending on the choice of solitonic parameters. A new inelastic collision phenomenon occurring in this system is that both the amplitudes of two components of each soliton get suppressed or enhanced after the collision, which might provide us with a different approach of signal amplification.

Analytic Studies on the Helmholtz Spatial Solitons in Power-Law Optical Materials

In order to describe refraction phenomena, the propagation of a spatial soliton in power-law optical materials is considered. Hereby, we work on the behavior of solitons described by a generalized nonlinear Helmholtz equation in the power-law optical materials. Via the Hirota method, analytic one- and two-soliton solutions are obtained. We study the spatial solitons in two adjoining power-law materials with dissimilar medium coefficients. Based on the choice of the Heaviside function in the equation, we distinguish the two different optical materials. One-soliton dynamics with different choices of the nonlinear and linear refractive properties along the propagation direction of the carrier wave are discussed. In the first medium, with an increase of the inverse width, the soliton will be amplified. In the second medium, the soliton amplitude will increase when the linear refractive property increases, or the nonlinear refractive property decreases. Asymptotic analysis is carried out on the two-soliton solutions. Through a graphic and asymptotic analysis, we find that there exist elastic and inelastic collisions between two solitons, as well as soliton fusion.

Multi-Soliton Solutions for an Inhomogeneous Nonlinear Schrödinger– Maxwell–Bloch System in the Erbium-Doped Fiber

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.