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

摘要

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