Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.

Higher-Order Rogue Wave Solutions to a Spatial Discrete Hirota Equation

The higher-order rogue wave （RW） for a spatial discrete Hirota equation is investigated by the generalized （1,N - 1）-fold Darboux transformation. We obtain the higher-order discrete RW solution to the spatial discrete Hirota equation. The fundamental RWs exhibit different amplitudes and shapes associated with the spectral parameters. The higher-order RWs display triangular patterns and pentagons with different peaks. We show the differences between the RW of the spatially discrete Hirota equation and the discrete nonlinear Schr6dinger equation. Using the contour line method, we study the localization characters including the length, width, and area of the first-order RWs of the spatially discrete Hirota equation.

Soliton solutions for a two-component generalized Sasa-Satsuma equation

As is well known,the Sasa-Satsuma equation is an important integrable high order nonlinear Schr?dinger equation.In this paper,a two-component generalized Sasa-Satsuma(g SS)equation is investigated.We construct the n-fold Darboux transformation for the two-component g SS equation.Based on the Darboux transformation,we obtain some interesting solutions,such as a breather soliton solution,kink solution,anti-soliton solution and a periodic-like solution.

Interactions of Soliton Waves for a Generalized Discrete KdV Equation

It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiserete integrable system （the time variable is continuous and the space one is discrete） that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system （the both of time and space variables are discrete） introduced by Kanki et al. In this paper, for the generalized discrete KdV （gdKdV） equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis.