Variational approximations in discrete nonlinear Schrِdinger equations with next-nearest-neighbor couplings

Solitons of a discrete nonlinear Schrِdinger equation which includes the next-nearest-neighbor (NNN) interactions are studied by means of a variational approximation (VA) and numerical computations. A large family of multi-humped solutions, including those with a nontrivial intrinsic phase structure, which is a feature particular to the system with the NNN interactions, are accurately predicted by the VA. Bifurcations linking solutions with the trivial and nontrivial phase structures are captured remarkably well by the analysis, including a prediction of the corresponding critical parameter values.