Approximated profiles for discrete solitons in DNLS lattices

TL;DR

This paper compares four approximation methods for determining discrete soliton profiles in the 1D DNLS equation, evaluating their accuracy against numerical solutions to identify the most effective approach.

Contribution

It introduces and compares three discrete and one quasi-continuum approximation methods for discrete solitons in the DNLS equation, providing insights into their relative effectiveness.

Findings

All approximations are evaluated against numerical solutions.

The study identifies which approximation best matches the numerical profiles.

Results highlight the strengths and limitations of each method.

Abstract

We study four different approximations for finding the profile of discrete solitons in the one-dimensional Discrete Nonlinear Schr\"odinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an approximation to homoclinic orbits and a Green-function approach), and the other one is a quasi-continuum approximation. All the results are compared with numerical computations.