Justification of the Lugiato-Lefever Model from a Damped Driven <i>ϕ</i><sup>4</sup> Equation

Justification of the Lugiato-Lefever Model from a Damped Driven <i>ϕ</i><sup>4</sup> Equation

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 th...

Full description

Bibliographic Details
Main Authors:	Fiki Taufik Akbar, Bobby Eka Gunara, Hadi Susanto
Format:	Article
Language:	English
Published:	MDPI AG 2020-05-01
Series:	Mathematics
Subjects:	Lugiato-Levefer equation nonlinear Schrödinger equation <i>ϕ</i><sup>4</sup> equation small-amplitude approximation
Online Access:	https://www.mdpi.com/2227-7390/8/5/727

Similar Items

Rogue waves in Lugiato-Lefever equation with variable coefficients
by: Kol Guy, et al.
Published: (2014-11-01)

pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation
by: Oliver Melchert, et al.
Published: (2021-07-01)

<i>L</i><sup><i>p</i></sup> Unit Spheres and the <i>α</i>-Geometries: Questions and Perspectives
by: Paolo Gibilisco
Published: (2020-12-01)

A Theoretical Study of Scattering of <i>e</i><sup>±</sup> by Tl Atom
by: Sunzida Parvin, et al.
Published: (2023-02-01)

Embracing [XY<sub>3</sub>]<i><sup>m–</sup></i> and [XY<sub>4</sub>]<i><sup>m–</sup></i> Anions in Salts of [M(bpy)<sub>3</sub>]<i><sup>q</sup></i><sup>+</sup>
by: Edwin C. Constable, et al.
Published: (2023-01-01)

Influence of <i>Clear<sup>T</sup></i> and <i>Clear<sup>T2</sup></i> Agitation Conditions in the Fluorescence Imaging of 3D Spheroids
by: Daniel N. Silva, et al.
Published: (2020-12-01)

Fixed point approach to solve fractional differential equations in S<sup>JS<sup>-metric spaces
by: Doaa Rizk, et al.
Published: (2022-06-01)

Associated Charmonium-Bottomonium Production in a Single Boson <i>e</i><sup>+</sup><i>e</i><sup>−</sup> Annihilation
by: Ilia Belov, et al.
Published: (2021-07-01)

Mycorrhizal Benefits of Salt-Stressed <i>Cinnamomum camphora</i> (L.) Presl. May Be Related to P and Mn<sup>2+</sup> Contents in Shoots, Biomass Allocation, and K<sup>+</sup>/Na<sup>+</sup> in Roots and Shoots
by: Yanhong Wang, et al.
Published: (2022-11-01)

L<i><sup>p</sup></i>-Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term
by: Juan Carlos Cortés, et al.
Published: (2020-06-01)

Characterization of Two Na<sup>+</sup>(K<sup>+</sup>, Li<sup>+</sup>)/H<sup>+</sup> Antiporters from <i>Natronorubrum daqingense</i>
by: Qi Wang, et al.
Published: (2023-06-01)

Targeting PirA<i><sup>vp</sup></i> and PirB<i><sup>vp</sup></i> Toxins of <i>Vibrio parahaemolyticus</i> with Oilseed Peptides: An In Silico Approach
by: Joe-Hui Ong, et al.
Published: (2021-10-01)

The Effect of Decreased Ca<sup>++</sup>/Mg<sup>++</sup> ATPase Activity on <i>Lactobacillus delbrueckii</i> subsp. <i>bulgaricus</i> sp1.1 Survival during Spray Drying
by: Jialei Sun, et al.
Published: (2023-02-01)

The two variable (<em>φ</em>'/<em>φ</em>, 1/<em>φ</em>)-expansion method for solving the time-fractional partial differential equations
by: Yunmei Zhao, et al.
Published: (2020-05-01)

Measurement of Aβ Amyloid Plaques and Tau Protein in Postmortem Human Alzheimer’s Disease Brain by Autoradiography Using [<sup>18</sup>F]Flotaza, [<sup>125</sup>I]IBETA, [<sup>124/125</sup>I]IPPI and Immunohistochemistry Analysis Using QuPath
by: Rommani Mondal, et al.
Published: (2023-03-01)

Solving Inverse Problem of Distributed-Order Time-Fractional Diffusion Equations Using Boundary Observations and <i>L</i><sup>2</sup> Regularization
by: Lele Yuan, et al.
Published: (2023-07-01)

Protection and Safety Evaluation of Live Constructions Derived from the Pgm<sup>−</sup> and pPCP1<sup>−</sup> <i>Yersinia pestis</i> Strain
by: Xiuran Wang, et al.
Published: (2020-02-01)

Heterotridentate Organomonophosphines in Pt(κ<sup>3</sup>–X<sup>1</sup>P<sup>1</sup>X<sup>2</sup>)(Y) (X<sup>1,2</sup> = N<sup>1,2</sup> or S<sup>1,2</sup>), Pt(κ<sup>3</sup>–P<sup>1</sup>N<sup>1</sup>X<sup>1</sup>)(Y) (X<sup>1</sup> = O, C, S or Se) Pt(κ<sup>3</sup>–P<sup>1</sup>S<sup>1</sup>Cl<sup>1</sup>)(Cl) and Pt(κ<sup>3</sup>–P<sup>1</sup>Si<sup>1</sup>N<sup>1</sup>)(OL)—Structural Aspects
by: Milan Melník, et al.
Published: (2022-12-01)

Mahgoub transform and Hyers-Ulam stability of n<sup>th</sup> order linear differential equations
by: S. Deepa, et al.
Published: (2022-01-01)

Fixed Point Results in <i>C</i><sup>🟉</sup>-Algebra-Valued Partial <i>b</i>-Metric Spaces with Related Application
by: Gunaseelan Mani, et al.
Published: (2023-02-01)

The Solvability of a System of Quaternion Matrix Equations Involving <i>ϕ</i>-Skew-Hermicity
by: Zhuo-Heng He, et al.
Published: (2022-06-01)

Structural Insights to the Heterotetrameric Interaction between the <i>Vibrio parahaemolyticus</i> PirA<i><sup>vp</sup></i> and PirB<i><sup>vp</sup></i> Toxins and Activation of the Cry-Like Pore-Forming Domain
by: Shin-Jen Lin, et al.
Published: (2019-04-01)

A Functional K<sup>+</sup> Channel from Tetraselmis Virus 1, a Member of the <i>Mimiviridae</i>
by: Kerri Kukovetz, et al.
Published: (2020-09-01)

<i>G</i><sup>2</sup> Hermite Interpolation by Segmented Spirals
by: Yuxuan Zhou, et al.
Published: (2022-12-01)

Global Landscapes of the <i>Na<sup>+</sup>/H<sup>+</sup> Antiporter (NHX)</i> Family Members Uncover their Potential Roles in Regulating the Rapeseed Resistance to Salt Stress
by: Jia-qian Cui, et al.
Published: (2020-05-01)

Processing of Fluorescent Proteins May Prevent Detection of Prion Particles in [<i>PSI</i><sup>+</sup>] Cells
by: Andrew G. Matveenko, et al.
Published: (2022-11-01)

<i>Populus euphratica</i> Phospholipase Dδ Increases Salt Tolerance by Regulating K<sup>+</sup>/Na<sup>+</sup> and ROS Homeostasis in Arabidopsis
by: Ying Zhang, et al.
Published: (2022-04-01)

Separability of the Planar 1/<i>ρ</i><sup>2</sup> Potential in Multiple Coordinate Systems
by: Richard DeCosta, et al.
Published: (2020-08-01)

NH<sub>4</sub><sup>+</sup> Toxicity, Which Is Mainly Determined by the High NH<sub>4</sub><sup>+</sup>/K<sup>+</sup> Ratio, Is Alleviated by CIPK23 in <i>Arabidopsis</i>
by: Sujuan Shi, et al.
Published: (2020-04-01)

On (<i>ϕ</i>, <i>ψ</i>)-Metric Spaces with Applications
by: Eskandar Ameer, et al.
Published: (2020-09-01)

<i>GhNHX3D</i>, a Vacuolar-Localized Na<sup>+</sup>/H<sup>+</sup> Antiporter, Positively Regulates Salt Response in Upland Cotton
by: Junping Feng, et al.
Published: (2021-04-01)

Dirichlet Problem with <i>L</i><sup>1</sup>(<i>S</i>) Boundary Values
by: Alexander G. Ramm
Published: (2022-07-01)

Comparison of the Therapeutic Effects of [<sup>211</sup>At]NaAt and [<sup>131</sup>I]NaI in an NIS-Expressing Thyroid Cancer Mouse Model
by: Tadashi Watabe, et al.
Published: (2022-08-01)

Depletion of Na<sup>+</sup>/H<sup>+</sup> Exchanger Isoform 1 Increases the Host Cell Resistance to <i>Trypanosoma cruzi</i> Invasion
by: João Paulo Ferreira Rodrigues, et al.
Published: (2022-11-01)

Phase I and II Clinical Trial Comparing the LBSap, Leishmune<sup>®</sup>, and Leish-Tec<sup>®</sup> Vaccines against Canine Visceral Leishmaniasis
by: Rodrigo Dian de Oliveira Aguiar-Soares, et al.
Published: (2020-11-01)

The Mechanism and Role of <i>N</i><sup>6</sup>-Methyladenosine (m<sup>6</sup>A) Modification in Atherosclerosis and Atherosclerotic Diseases
by: Quandan Tan, et al.
Published: (2022-10-01)

The Organization of Pericentromeric Heterochromatin in Polytene Chromosome 3 of the <i>Drosophila</i> <i>melanogaster</i> Line with the <i>Rif1<sup>1</sup>; SuUR<sup>ES</sup> Su(var)3-9<sup>06</sup></i> Mutations Suppressing Underreplication
by: Tatyana Zykova, et al.
Published: (2021-10-01)

Spinach Plants Favor the Absorption of K<sup>+</sup> over Na<sup>+</sup> Regardless of Salinity, and May Benefit from Na<sup>+</sup> When K<sup>+</sup> is Deficient in the Soil
by: Jorge F. S. Ferreira, et al.
Published: (2020-04-01)

Ontogenetic Development of Gill and Na<sup>+</sup>/K<sup>+</sup> ATPase in the Air-Breathing Loach
by: Yaqiu Liu, et al.
Published: (2022-12-01)

Na<sup>+</sup>,K<sup>+</sup>-ATPase with Disrupted Na<sup>+</sup> Binding Sites I and III Binds Na<sup>+</sup> with Increased Affinity at Site II and Undergoes Na<sup>+</sup>-Activated Phosphorylation with ATP
by: Hang N. Nielsen, et al.
Published: (2024-01-01)