Gap and out-gap solitons in modulated systems of finite length: exact solutions in the slowly varying envelope limit
2011 (English)In: PHYSICA SCRIPTA, ISSN 0031-8949, Vol. 83, no 6Article in journal (Refereed) Published
We discuss nonlinear excitations in finite-size one-dimensional modulated systems. Considering a binary modulated discrete nonlinear Schrodinger chain of large but finite length with periodic boundary conditions, we obtain exact elliptic-function solutions corresponding to stationary excitations in the slowly varying envelope limit. From these solutions, we analyze how the transformation between (localized) gap and (delocalized) out-gap solitons manifests itself in a system of finite length. The analogue of a localized gap soliton appears through a bifurcation at a critical point, so that gap soliton analogues exist only for chains longer than a critical value, which scales inversely proportional to the modulation depth. The total norm of these gap-out-gap states is found to be a monotonic function of the frequency, always inside a nonlinear gap with edges defined by the main nonlinear modes which approach the linear spectrum gap boundaries in the small-amplitude limit. The transformation from a gap to an out-gap state is associated with a particular frequency, close to the lower boundary of the linear gap; at this point the elliptic functions become trigonometric, corresponding to a finite-size analogue of an algebraic soliton. We compare the scenario with earlier results obtained numerically for purely discrete chains with few degrees of freedom.
Place, publisher, year, edition, pages
Royal Swedish Academy of Sciences , 2011. Vol. 83, no 6
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-69166DOI: 10.1088/0031-8949/83/06/065005ISI: 000291153700005OAI: oai:DiVA.org:liu-69166DiVA: diva2:424343