Solitons of a simple nonlinear model on the cubic lattice

TL;DR

This paper investigates a nonlinear lattice model, introduces a bilinearization method linking it to known integrable systems, and derives explicit N-soliton solutions, advancing understanding of discrete nonlinear phenomena.

Contribution

It presents a new bilinearization scheme for a simple nonlinear cubic lattice model, connecting it to established integrable systems and deriving explicit N-soliton solutions.

Findings

The model is closely related to Hirota and Ablowitz-Ladik systems.

Explicit N-soliton solutions are derived.

The bilinearization approach simplifies analysis of the nonlinear lattice.

Abstract

We study a simple nonlinear model defined on the cubic lattice. 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 the N-soliton solutions.