Data di Pubblicazione:
2018
Citazione:
On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice / T. Penati, M. Sansottera, S. Paleari, K. V., K. P. G.. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 370(2018 May 01), pp. 1-13.
Abstract:
We consider a one-dimensional discrete nonlinear Schrödinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-sites vortex solutions in the standard two-dimensional dNLS model (square lattice), of which this is a simpler variant. Due to the specific choice of lengths of the inter-site interactions, the vortex configurations considered present a degeneracy which causes the standard continuation techniques to be non-applicable.
In the present one-dimensional case, the existence of a conserved quantity for the soliton profile (the so-called density current), together with a perturbative construction, leads to the nonexistence of any phase-shift discrete soliton which is at least C2 with respect to the small coupling ϵ, in the limit of vanishing ϵ. If we assume the solution to be only C0 in the same limit of ϵ, nonexistence is instead proved by studying the bifurcation equation of a Lyapunov-Schmidt reduction, expanded to suitably high orders. Specifically, we produce a nonexistence criterion whose efficiency we reveal in the cases of partial and full degeneracy of approximate solutions obtained via a leading order expansion.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Discrete non-linear Schrodinger; Discrete solitons; Discrete vortex; Current conservation; Perturbation theory; Lyapunov-Schmidt decomposition
Elenco autori:
T. Penati, M. Sansottera, S. Paleari, K. V., K. P. G.
Link alla scheda completa: