Two-Dimensional Toda-Heisenberg Lattice

TL;DR

This paper introduces a new 2D nonlinear lattice model combining Heisenberg and Toda features, derives its bilinear form via Hirota's method, and constructs its N-soliton solutions.

Contribution

It presents a novel 2D lattice model and provides explicit N-soliton solutions using Hirota's direct approach, linking it to the Ablowitz-Ladik hierarchy.

Findings

Derived bilinear form of the model

Constructed explicit N-soliton solutions

Connected the model to Ablowitz-Ladik hierarchy

Abstract

We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.