463 research outputs found

    The Bilinear Formula in Soliton Theory of Optical Fibers

    Get PDF
    Solitons are wave phenomena or pulses that can maintain their shape stability when propagating in a medium. In optical fibers, they become general solutions of the Non-Linear Schrödinger Equation (NLSE). Despite its mathematical complexity, NLSE has been an interesting issue. Soliton analysis and mathematical techniques to solve problems of the equation keep doing. Yan Chen (2022) introduced them based on bilinear formula for the case of the generalized NLSE extended models into third and fourth-order dispersions and cubic-quintic nonlinearity. In this paper, we review the form of the bilinear formula for the case. We re-observed a one-soliton solution based on the formula and verified the work of the last researcher. Here, the mathematical parameters of position α(0) and phase η are verified to become features of change in horizontal position and phase of one soliton in the (z, t) plane during propagation. In addition, we notice the soliton has established stability. Finally, for the condition Kerr effect focusing or the group velocity dispersion β2 more dominates, we present like the soliton trains in optical fibers under modulation instability of plane wave

    Localized and periodic wave patterns for a nonic nonlinear Schrodinger equation

    Get PDF
    postprin

    The hierarchy of rogue wave solutions in nonlinear systems

    Get PDF
    Oceanic freak waves, optical spikes and extreme events in numerous contexts can arguably be modelled by modulationally unstable solutions within nonlinear systems. In particular, the fundamental nonlinear Schroedinger equation (NLSE) hosts a high-amplitude spatiotemporally localised solution on a plane-wave background, called the Peregrine breather, which is generally considered to be the base-case prototype of a rogue wave. Nonetheless, until very recently, little was known about what to expect when observing or engineering entire clusters of extreme events. Accordingly, this thesis aims to elucidate this matter by investigating complicated structures formed from collections of Peregrine breathers. Many novel NLSE solutions are discovered, all systematically classifiable by their geometry. The methodology employed here is based on the well-established concept of Darboux transformations, by which individual component solutions of an integrable system are nonlinearly superimposed to form a compound wavefunction. It is primarily implemented in a numerical manner within this study, operating on periodically modulating NLSE solutions called breathers. Rogue wave structures can only be extracted at the end of this process, when a limit of zero modulation frequency is applied to all components. Consequently, a requirement for breather asymmetry ensures that a multi-rogue wavefunction must be formed from a triangular number of individual Peregrine breathers (e.g. 1, 3, 6, 10, ...), whether fused or separated. Furthermore, the arrangements of these are restricted by a maximum phase-shift allowable along an evolution trajectory through the relevant wave field. Ultimately, all fundamental high-order rogue wave solutions can be constructed via polynomial relations between origin-translating component shifts and squared modulation frequency ratios. They are simultaneously categorisable by both these mathematical existence conditions and the corresponding visual symmetries, appearing spatiotemporally as triangular cascades, pentagrams, heptagrams, and so on. These parametric relations do not conflict with each other, meaning that any arbitrary NLSE rogue wave solution can be considered a hybridisation of this elementary set. Moreover, this hierarchy of structures is significantly general, with complicated arrangements persisting even on a cnoidal background

    Light Beams in Liquid Crystals

    Get PDF
    This reprint collects recent articles published on "Light Beams in Liquid Crystals", both research and review contributions, with specific emphasis on liquid crystals in the nematic mesophase. The editors, Prof. Gaetano Assanto (NooEL, University of Rome "Roma Tre") and Prof. Noel F. Smyth (School of Mathematics, University of Edinburgh), are among the most active experts worldwide in nonlinear optics of nematic liquid crystals, particularly reorientational optical solitons ("nematicons") and other all-optical effects

    Three-dimensional topological solitons in PT-symmetric optical lattices

    Get PDF
    We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.Peer ReviewedPostprint (published version

    Light Beams in Liquid Crystal

    Get PDF

    Phase dynamics of the dysthe equation and the bifurcation of plane waves

    Get PDF
    The bifurcation of plane waves to localised structures is investigated in the Dysthe equation, which incorporates the effects of mean flow and wave steepening. Through the use of phase modulation techniques, it is demonstrated that such occurrences may be described using a Korteweg–de Vries equation. The solitary wave solutions of this system form a qualitative prototype for the bifurcating dynamics, and the role of mean flow and steepening is then made clear through how they enter the amplitude and width of these solitary waves. In addition, higher order phase dynamics are investigated, leading to increased nonlinear regimes which in turn have a more profound impact on how the plane waves transform under defects in the phase
    • …
    corecore