Variational approximations in discrete nonlinear Schr\"odinger equations with next-nearest-neighbor couplings

TL;DR

This paper investigates discrete nonlinear Schrödinger equations with next-nearest-neighbor couplings, using variational approximation and numerical methods to predict complex soliton solutions and bifurcations.

Contribution

It introduces a variational approximation that accurately predicts multi-humped solutions and bifurcations in models with next-nearest-neighbor interactions.

Findings

Accurate prediction of multi-humped solutions

Identification of bifurcation points and phase structures

Validation of variational approximation against numerical results

Abstract

Solitons of a discrete nonlinear Schr\"{o}dinger equation which includes the next-nearest-neighbor interactions are studied by means of a variational approximation and numerical computations. A large family of multi-humped solutions, including those with a nontrivial phase structure which are a feature particular to the next-nearest-neighbor interaction model, are accurately predicted by the variational approximation. Bifurcations linking solutions with the trivial and nontrivial phase structures are also captured remarkably well, including a prediction of critical parameter values.