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Nonlinear differential equation with non-local coupling for a helical optical waveguide

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  • Bocharov, Andrey A.

Abstract

A helical optical waveguide with small values of the transverse size of the waveguide and the helical pitch relative to its radius is considered. There is a Kerr-type nonlinearity in the system. Such a system results in a differential equation with the positive and negative shifts in evolutionary argument. The paper presents solutions to the evolutionary problem for such an equation. The fundamental difficulties in obtaining such solutions in the highly nonlinear case are discussed. Breather solutions are presented for time-localized initial data.

Suggested Citation

  • Bocharov, Andrey A., 2026. "Nonlinear differential equation with non-local coupling for a helical optical waveguide," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017254
    DOI: 10.1016/j.chaos.2025.117712
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    References listed on IDEAS

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    1. Bocharov, A.A., 2023. "Topological edge solitons in the non-Hermitian nonlinear Su-Schrieffer-Heeger model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Bocharov, Andrey A., 2023. "Stationary states and dynamic regimes for a nonlinear asymmetric trimer with gain and loss," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Mikael C. Rechtsman & Julia M. Zeuner & Yonatan Plotnik & Yaakov Lumer & Daniel Podolsky & Felix Dreisow & Stefan Nolte & Mordechai Segev & Alexander Szameit, 2013. "Photonic Floquet topological insulators," Nature, Nature, vol. 496(7444), pages 196-200, April.
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