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AuthorPenati T.
AuthorSansottera M.
AuthorPaleari S.
AuthorKoukouloyannis V.
AuthorKevrekidis P.G.
Available date2019-10-06T09:38:36Z
Publication Date2018
Publication NamePhysica D: Nonlinear Phenomena
ResourceScopus
ISSN0167-2789
URIhttp://dx.doi.org/10.1016/j.physd.2017.12.012
URIhttp://hdl.handle.net/10576/12100
AbstractWe consider a one-dimensional discrete nonlinear Schrdinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-site 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 in the limit of vanishing . If we assume the solution to be only C0 in the same limit of 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.
SponsorWe thank Prof.Dmitry Pelinovsky for the helpful discussions on the proof of Lemma 4.4 that we had during the SIAM conference on Nonlinear Waves and Coherent Structures. This work has been partially supported by NSF - PHY-1602994 (PGK). Also, VK and PGK acknowledge that this work made possible by NPRP grant # [9-329-1-067] from Qatar National Research Fund (a member of Qatar Foundation). Appendix A
Languageen
PublisherElsevier B.V.
SubjectCurrent conservation
Discrete non-linear Schr?dinger
Discrete solitons
Discrete vortex
Lyapunov Schmidt decomposition
Perturbation theory
TitleOn the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice
TypeArticle
Pagination1
Volume Number370
dc.accessType Abstract Only


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