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

Mathematics

Hadi Susanto¹  BobbyEka Gunara²  FikiTaufik Akbar² 

[1] Department of Mathematics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK;Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia;

关键词: Lugiato-Levefer equation;    nonlinear Schrödinger equation;    ϕ⁴ equation;    small-amplitude approximation;   

DOI  :  10.3390/math8050727

来源: DOAJ

【 摘 要 】

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 ${\varphi }^4$ 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.

【 授权许可】

Unknown