Stability of gap solitons in the presence of a weak nonlocality in periodic potentials
In this work, we study the stability and internal modes of one-dimensional gap solitons employing the modified nonlinear Schrödinger equation with a sinusoidal potential together with the presence of a weak nonlocality. Using an analytical theory, it is proved that two soliton families bifurcate out...
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Published in | The European physical journal. ST, Special topics Vol. 225; no. 6-7; pp. 1187 - 1197 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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Springer Berlin Heidelberg
01.09.2016
Springer Nature B.V |
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Abstract | In this work, we study the stability and internal modes of one-dimensional gap solitons employing the modified nonlinear Schrödinger equation with a sinusoidal potential together with the presence of a weak nonlocality. Using an analytical theory, it is proved that two soliton families bifurcate out from every Bloch-band edge under self-focusing or self-defocusing nonlinearity, and one of these is always unstable. Also we study the oscillatory instabilities and internal modes of the modified nonlinear Schrödinger equation. |
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AbstractList | In this work, we study the stability and internal modes of one-dimensional gap solitons employing the modified nonlinear Schrödinger equation with a sinusoidal potential together with the presence of a weak nonlocality. Using an analytical theory, it is proved that two soliton families bifurcate out from every Bloch-band edge under self-focusing or self-defocusing nonlinearity, and one of these is always unstable. Also we study the oscillatory instabilities and internal modes of the modified nonlinear Schrödinger equation. |
Author | Rothos, V.M. Rossides, A.K. Mylonas, I.K. |
Author_xml | – sequence: 1 givenname: I.K. surname: Mylonas fullname: Mylonas, I.K. organization: Department of Mechanical Engineering, Laboratory of Nonlinear Dynamics, Aristotle University of Thessaloniki – sequence: 2 givenname: A.K. surname: Rossides fullname: Rossides, A.K. organization: Oceanography Center, University of Cyprus – sequence: 3 givenname: V.M. surname: Rothos fullname: Rothos, V.M. email: rothos@auth.gr organization: Department of Mechanical Engineering, Laboratory of Nonlinear Dynamics, Aristotle University of Thessaloniki |
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Cites_doi | 10.1103/PhysRevE.64.016612 10.1109/JQE.1968.1074930 10.1103/PhysRevE.63.016610 10.1364/OL.28.000251 10.1088/0305-4470/34/45/302 10.1364/OL.35.002152 10.1063/1.1652612 10.1063/1.126859 10.1098/rspa.2011.0341 10.1098/rspa.2000.0526 10.1364/OL.27.001460 10.1111/sapm.12057 10.1364/OL.17.000475 10.1137/1.9780898719680 10.1016/j.physd.2011.03.003 10.1103/RevModPhys.71.463 10.1103/PhysRevA.48.611 10.1103/PhysRevE.70.036618 10.1103/PhysRevA.48.4583 10.1016/0167-2789(96)00069-3 10.1063/1.1713919 10.1103/PhysRevE.62.4300 10.1103/PhysRevA.37.3557 10.1103/PhysRevLett.95.053904 10.1016/j.physd.2005.07.021 10.1143/JPSJ.42.1824 10.1103/PhysRevA.78.063812 10.1111/j.1467-9590.2011.00538.x 10.1103/PhysRevA.57.R3180 10.1088/1464-4266/6/5/017 10.1103/PhysRevA.61.051601 10.1103/PhysRevLett.98.263902 10.1103/PhysRevE.66.066615 |
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SubjectTerms | Atomic Bifurcation theory Classical and Continuum Physics Condensed Matter Physics Defocusing Materials Science Mathematical Modeling of Complex Systems Measurement Science and Instrumentation Molecular Nonlinearity Optical and Plasma Physics Physics Physics and Astronomy Regular Article Schrodinger equation Solitary waves Stability |
Title | Stability of gap solitons in the presence of a weak nonlocality in periodic potentials |
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