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    Effect of higher-order dispersion on modulation instability, soliton propagation and pulse splitting
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Demircan, Ayhan; Pietrzyk, Monika; Bandelow, Uwe
    By solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in highly nonlinear fibers. In the anomalous dispersion regime third-order dispersion can, in general, induce soliton fission and yields asymmetric spectra, whereas modulation instability can be slightly suppressed. In the normal dispersion regime we demonstrate pulse splitting by third-order dispersion, as well as its later suppression by fourth-order dispersion.
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    On the propagation of vector ultra-short pulses
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pietrzyk, Monika; Kanattsikov, I.; Bandelow, Uwe
    A two component vector generalization of the Schäfer-Wayne short pulse equation which describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization is presented. As a special case, the integrable two-component short pulse equations are constructed which represent the counterpart of the Manakov system in the case of ultra-short pulses.
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    Multisymplectic analysis of the short pulse equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Pietrzyk, Monika; Kanattsikov, Igor
    The multisymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric multisymplectic integrator of it. A brief comparison of its effectiveness relative to the pseudo-spectral integration scheme is presented.
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    Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Bhattacharjee, Aranya; Pietrzyk, Monika
    The Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice is investigated. We show that the effective mass increases in an optical superlattice, which leads to localization of the BEC, in accordance with recent experimental observations [17]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.