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Has files: Yes × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: solitons ×

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Now showing 1 - 6 of 6
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    Persistence of rouge waves in extended nonlinear Schrödinger equations : integrable Sasa-Satsuma case
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Bandelow, Uwe; Akhmediev, Nail N.
    We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.
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    Simulation of pulse propagation in nonlinear optical fibers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Bandelow, Uwe; Demircan, Ayhan; Kesting, Martin
    We solve numerically a generalized nonlinear Schroedinger equation by using a pseudospectral method. Integration is performed by using an eight-order Runge-Kutta scheme. The numerical method therefore differs from the commonly used split-step method. Effects such as the impact of group velocity dispersion (GVD) up to fourth-order dispersion, self phase modulation (SPM), self-steepening and intrapulse Raman scattering can be investigated with the code. Examples for the above effects are demonstrated, as well as their interplay in the context of soliton propagation and sub-picosecond pulses.
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    Stabilization of optical pulse transmission by exploiting fiber nonlinearities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Bandelow, Uwe; Amiranashvili, Shalva; Pickartz, Sabrina
    We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.
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    Multi-stability and polariton formation in microcavity polaritonic waveguides
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Slavcheva, Gabriela; Gorbach, Andrey V.; Pimenov, Alexander; Vladimirov, Andrei G.; Skryabin, Dmitry
    Nonlinear polaritons in microcavity waveguides are demonstrated to exhibit multi-stable behaviour and rich dynamics, including filamentation and soliton formation. We find that the multi-stability originates from co-existense of different transverse modes of the polaritonic waveguide. Modulational stability and conditions for multi-mode polariton solitons are studied. Soliton propagation in tilted, relative to the pump momentum, waveguides is demonstrated and a critical tilt angle for the soliton propagation is found.
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    The impact of microcavity wire width on polariton soliton existence and multistability
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Slavcheva, Gabriela; Koleva, Mirella V.; Pimenov, Alexander
    We have developed a model of the nonlinear polariton dynamics in realistic 3D non-planar microcavity wires in the driven-dissipative regime [15]. We find that the typical microcavity optical bistability evolves into multi-stability upon variation of the model parameters. The origin of the multi-stability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multi-mode polariton solitons in the triggered parametric oscillator regime. Further, we demonstrate stable polariton soliton propagation in tilted and tapered waveguides, and determine maximum tilt angles for which solitons are still found. Additionally, we study soliton amplitude and velocity dependence on the wire width, with a view towards device applications.
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    Generalized Sasa-Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Ankiewicz, Adrian; Bandelow, Uwe; Akhmediev, Nail
    We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 x3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.