Soliton dynamics in a 2D lattice model with nonlinear interactions

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-Petviashviii I type which allows the explicit construction of moving multi-solitons on the lattice. Numerical simulation performed at the discrete system investigates the stability and dynamics of the multi-soliton in the lattice space.