Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials

TL;DR

This paper investigates how linear and nonlinear periodic potentials influence the stability and dynamics of bright solitary waves, using analytical and numerical methods to predict their behavior.

Contribution

It introduces a perturbative Hamiltonian approach to analyze the existence and stability of solitary waves in combined linear and nonlinear lattices.

Findings

Analytical results align well with numerical simulations.

Conditions for stability are derived from eigenvalue analysis.

Predictions about dynamical evolution are validated numerically.

Abstract

In this paper, we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtained detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions.