Exact solutions and linear stability analysis for two-dimensional Ablowitz–Ladik equation

Abstract

Abstract:The Ablowitz-Ladik equation is a very important model in the nonlinear mathematical physics. In this paper, the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions and the rational wave solutions with more arbitrary parameters of 2-dimensional Ablowitz-Ladik equation are derived by using the (G'/G )-expansion method, and the effect of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions is analysed and numerically simulated.

Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

“…The bright and dark soliton solutions of a AL equation are obtained via the Hirota bilinear method in Ref. [50]. However, the 2+1-dimensional NDBDSSs and their interactions of the AL equation have not been studied, we will analyze the soliton dynamics of Eq.…”