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Subject: Nonlinear Schrödinger Equations ×

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    Self-compression of 120 fs pulses in a white-light filament
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Bethge, Jens; Steinmeyer, Günter; Stibenz, Gero; Staudt, Peter; Brée, Carsten; Demircan, Ayhan; Redlin, Harald; Düsterer, Stefan
    Self-compression of pulses with >100 fs input pulse duration from a 10 Hz laser system is experimentally demonstrated, with a compression factor of 3.3 resulting in output pulse durations of 35 fs. This measurement substantially widens the range of applicability of this compression method, enabling self-compression of pulsed laser sources that neither exhibit extremely low pulse-to-pulse energy fluctuations nor a particularly clean beam profile. The experimental demonstration is numerically modeled, revealing the exact same mechanisms at work as at shorter input pulse duration. Additionally, the role of controlled beam clipping with an adjustable aperture is numerically substantiated
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    Infinite hierarchy of nonlinear Schrödinger equations and Infinite hierarchy of nonlinear Schrödinger equations and
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ankiewicz, Adrian; Kedziora, David Jacob; Chowdury, Amdad; Bandelow, Uwe; Nail Akhmediev, Nail
    We study the infinite integrable nonlinear Schrödinger equation (NLSE) hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, AB breathers, Kuznetsov-Ma breathers, periodic solutions and rogue wave solutions for this infinite order hierarchy. We find that even order equations in the set affect phase and stretching factors in the solutions, while odd order equations affect the velocities. Hence odd order equation solutions can be real functions, while even order equation solutions are always complex.