Variational Approximations of Bifurcations of Asymmetric Solitons in Cubic-Quintic Nonlinear Schroedinger Lattices

TL;DR

This paper uses a variational approximation with six parameters to analyze bifurcations and stability exchanges of asymmetric discrete solitons in a cubic-quintic nonlinear Schrödinger lattice, showing good agreement with numerical results for small powers.

Contribution

It introduces a six-parameter variational ansatz to effectively approximate bifurcations and stability exchanges of asymmetric solitons in the lattice.

Findings

Variational approximation closely matches numerical results for small soliton powers.

Bifurcations connect site-centered and bond-centered solutions.

Stability exchanges are accurately captured by the variational method.

Abstract

Using a variational approximation we study discrete solitons of a nonlinear Schroedinger lattice with a cubic-quintic nonlinearity. Using an ansatz with six parameters we are able to approximate bifurcations of asymmetric solutions connecting site-centered and bond-centered solutions and resulting in the exchange of their stability. We show that the numerically exact and variational approximations are quite close for solitons of small powers.