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    Area of Science:

    • Nonlinear Optics
    • Mathematical Physics
    • Wave Propagation

    Background:

    • The nonlinear Schrödinger equation (NLSE) is fundamental for modeling wave phenomena in various physical systems.
    • Understanding the behavior of generalized NLSE with higher-order dispersion terms is crucial for advanced applications.
    • Periodic traveling wave solutions, particularly dn-oidal-like solutions, are important for describing stable wave patterns.

    Purpose of the Study:

    • To investigate a family of periodic traveling wave solutions for a pure quartic generalized nonlinear Schrödinger equation (NLSE).
    • To analyze the modulational instability of these solutions.
    • To determine the conditions under which stable, regular, and comb-like spectral propagation can be observed in optical waveguides.

    Main Methods:

    • Numerical computation of a one-parameter family of dn-oidal-like solutions.
    • Comparison of these solutions with their conventional NLSE counterparts.
    • Numerical analysis of the modulational instability problem for the generalized NLSE.

    Main Results:

    • A one-parameter family of dn-oidal-like solutions with a nonzero average component was numerically identified.
    • Modulational instability analysis revealed a nontrivial trend: instability occurs in specific parameter intervals separated by stability islands.
    • Numerical simulations confirmed the existence of stable propagation regimes.

    Conclusions:

    • High-order dispersion terms in optical waveguides enable the observation of regular and stable comb-like spectra.
    • The identified stability islands offer potential for controlling and utilizing complex wave phenomena in nonlinear systems.