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Justification of the Lugiato-Lefever Model from a Damped Driven ϕ 4 Equation

Author

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  • Fiki Taufik Akbar

    (Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia)

  • Bobby Eka Gunara

    (Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia)

  • Hadi Susanto

    (Department of Mathematics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK)

Abstract

The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schrödinger equation. It is a mathematical model describing complex phenomena in dissipative and nonlinear optical cavities. Within the last two decades, the equation has gained much attention as it has become the basic model describing microresonator (Kerr) frequency combs. Recent works derive the Lugiato-Lefever equation from a class of damped driven ϕ 4 equations closed to resonance. In this paper, we provide a justification of the envelope approximation. From the analysis point of view, the result is novel and non-trivial as the drive yields a perturbation term that is not square integrable. The main approach proposed in this work is to decompose the solutions into a combination of the background and the integrable component. This paper is the first part of a two-manuscript series.

Suggested Citation

  • Fiki Taufik Akbar & Bobby Eka Gunara & Hadi Susanto, 2020. "Justification of the Lugiato-Lefever Model from a Damped Driven ϕ 4 Equation," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:727-:d:354296
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    References listed on IDEAS

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    1. P. Del’Haye & A. Schliesser & O. Arcizet & T. Wilken & R. Holzwarth & T. J. Kippenberg, 2007. "Optical frequency comb generation from a monolithic microresonator," Nature, Nature, vol. 450(7173), pages 1214-1217, December.
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