Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather

TL;DR

This paper constructs a nonlinear lattice with a specific potential symmetry that facilitates smooth propagation of discrete breathers, providing explicit solutions and an algorithm for numerical computation.

Contribution

It introduces a novel symmetric nonlinear lattice with explicit Hamiltonian and algebraic conditions, enabling improved numerical analysis of discrete breathers.

Findings

Unique solution to algebraic symmetry conditions

Explicit Hamiltonian for the symmetric lattice

Effective algorithm for computing traveling discrete breathers

Abstract

We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of the potential function with respect to a map acting on the complex normal mode coordinates. Condition of the symmetry is given by a set of algebraic equations with respect to coefficients of the pairwise interactions. We prove that the set of algebraic equations has a unique solution, and moreover we solve it explicitly. We present an explicit Hamiltonian for the symmetric lattice, which has coefficients given by the solution. We demonstrate that the present symmetric lattice is useful for numerically computing traveling discrete breathers in various lattices. We propose an algorithm using it.