Surface gap solitons at a nonlinearity interface

Details Surface gap solitons at a nonlinearity interface Surface gap solitons at a nonlinearity interface

2007-04-13

arxiv.org/abs/0704.1742v2

Nonlinear Sciences

Pattern Formation and Solitons

23 pages, 6 figures, 3 tables corrections in v.2: sign error in the energy functional on p.3; discussion of the symmetries of

Scientific paper

10.1137/060676751

We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross--Pitaevsky equation. We call these waves the surface gap solitons (SGS). In the case of smooth symmetric periodic potentials, we study analytically bifurcations of SGS's from standard gap solitons and determine numerically the maximal jump of the nonlinearity coefficient allowing for the SGS existence. We show that the maximal jump vanishes near the thresholds of bifurcations of gap solitons. In the case of continuous potentials with a jump in the first derivative at the interface, we develop a homotopy method of continuation of SGS families from the solution obtained via gluing of parts of the standard gap solitons and study existence of SGS's in the photonic band gaps. We explain the termination of the SGS families in the interior points of the band gaps from the bifurcation of linear bound states in the continuous non-smooth potentials.

Affiliated with

Also associated with

No associations

Rating

Surface gap solitons at a nonlinearity interface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Surface gap solitons at a nonlinearity interface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surface gap solitons at a nonlinearity interface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-678367