Soliton Dynamics in a 2D Lattice Model with Nonlinear Interactions

TL;DR

This paper investigates soliton solutions in a 2D lattice model with nonlinear interactions, analyzing their stability and dynamics through continuum approximation and numerical simulations, revealing integrable behavior akin to KP I equations.

Contribution

It introduces a 2D lattice model with nonlinear, competing interactions and derives an asymptotic continuum approximation that captures soliton dynamics and stability.

Findings

Long-time evolution governed by KP I type equation

Explicit construction of moving multi-solitons

Numerical simulations confirm soliton stability and dynamics

Abstract

This paper is concerned with a lattice model which is suited to square-rectangle transformations characterized by two strain components. The microscopic model involves nonlinear and competing interactions, which play a key role in the stability of soliton solutions and emerge from interactions as a function of particle pairs and noncentral type or bending forces. Special attention is devoted to the continuum approximation of the two-dimensional discrete system with the view of including the leading discreteness effects at the continuum description. The long time evolution of the localized structures is governed by an asymptotic integrable equation of the Kadomtsev-Petviashvili I type which allows the explicit construction of moving multi-solitons on the lattice. Numerical simulation performed at the discrete system investigate the stability and dynamics of multi-soliton in the lattice space.