# The exact solutions and their linear stability analysis for 2-dimensional Ablowitz-Ladik equation

## TL;DR

This paper derives exact solutions for the 2D Ablowitz-Ladik equation, analyzes their linear stability considering various parameters, and supports findings with numerical simulations, advancing understanding of this important nonlinear model.

## Contribution

It introduces new explicit solutions for the 2D Ablowitz-Ladik equation and investigates their stability influenced by multiple parameters.

## Key findings

- Hyperbolic, trigonometric, and rational wave solutions derived
- Parameter effects on stability analyzed and simulated
- Numerical results support stability analysis

## 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 GG-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.

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Source: https://tomesphere.com/paper/1701.06166