Explicit solutions for a nonlinear model on the honeycomb and triangular lattices

TL;DR

This paper derives explicit solutions for a nonlinear lattice model on honeycomb and triangular structures by linking it to known integrable systems, providing N-soliton and Toeplitz determinant solutions.

Contribution

It introduces a bilinearization scheme for the nonlinear model and connects it to established integrable models, enabling explicit solution construction.

Findings

Derived N-soliton solutions for the nonlinear lattice model.

Constructed solutions using Toeplitz determinants.

Linked the model to Hirota and Ablowitz-Ladik systems.

Abstract

We study a simple nonlinear model defined on the honeycomb and triangular lattices. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik system. This result is used to derive the two sets of explicit solutions: the N-soliton solutions and ones constructed of the Toeplitz determinants.