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The appearance of gap solitons in a nonlinear Schrodinger lattice
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-6708-1560
National Acadamy of Science Ukraine.
National Acadamy of Science Ukraine.
2010 (English)In: PHYSICA D-NONLINEAR PHENOMENA, ISSN 0167-2789, Vol. 239, no 5, 269-278 p.Article in journal (Refereed) Published
Abstract [en]

We study the appearance of discrete gap solitons in a nonlinear Schrodinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q = pi/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this "nonlinear gap boundary" are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gal) edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.

Place, publisher, year, edition, pages
2010. Vol. 239, no 5, 269-278 p.
Keyword [en]
Discrete gap solitons, Bifurcations, Linear stability, Thermalization
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-53814DOI: 10.1016/j.physd.2009.11.007ISI: 000273924200004OAI: oai:DiVA.org:liu-53814DiVA: diva2:292191
Available from: 2010-02-05 Created: 2010-02-05 Last updated: 2014-01-13

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Kroon, LarsJohansson, Magnus

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