Justification of the Lugiato-Lefever model from a damped driven $ϕ^4$ equation
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| Format: | Preprint |
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2018
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| _version_ | 1866929461937569792 |
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| author | Akbar, Fiki T. Gunara, Bobby E. Susanto, Hadi |
| author_facet | Akbar, Fiki T. Gunara, Bobby E. Susanto, Hadi |
| contents | 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 a wide attention as it becomes the basic model describing optical 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1810_10630 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Justification of the Lugiato-Lefever model from a damped driven $ϕ^4$ equation Akbar, Fiki T. Gunara, Bobby E. Susanto, Hadi Mathematical Physics Analysis of PDEs 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 a wide attention as it becomes the basic model describing optical 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. |
| title | Justification of the Lugiato-Lefever model from a damped driven $ϕ^4$ equation |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/1810.10630 |