Justification of the Lugiato-Lefever Model from a Damped Driven ϕ4 Equation

Fiki Taufik Akbar, Bobby Eka Gunara, Hadi Susanto

Research output: Contribution to journalArticlepeer-review


The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schrodinger 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 ϕ4 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.

Original languageBritish English
Article number727
Issue number5
StatePublished - 1 May 2020


  • Lugiato-lefever equation
  • Nonlinear schrödinger equation
  • Small-amplitude approximation
  • ϕ equation


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