Stability of a stationary solution for the Lugiato-Lefever equation

DOI10.2748/tmj/1325886285zbMath1234.35251OpenAlexW2063858530MaRDI QIDQ765673

Isamu Ohnishi, Tomoyuki Miyaji, Yoshio Tsutsumi

Publication date: 21 March 2012

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1325886285

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides ⋮ Periodic waves of the Lugiato–Lefever equation at the onset of Turing instability ⋮ Steady-state mode interactions of radially symmetric modes for the Lugiato-Lefever equation on a disk ⋮ Linear modulational and subharmonic dynamics of spectrally stable Lugiato-Lefever periodic waves ⋮ The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption ⋮ Nonlinear modulational dynamics of spectrally stable Lugiato-Lefever periodic waves ⋮ Erratum to: ``Stability of stationary solution for the Lugiato-Lefever equation ⋮ On the Generation of Stable Kerr Frequency Combs in the Lugiato--Lefever Model of Periodic Optical Waveguides

Cites Work

• Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
• Continuous and discrete dynamics near manifolds of equilibria
• Dissipative solitons. From optics to biology and medicine
• Finite dimensional behavior for weakly damped driven Schrödinger equations
• Geometric theory of semilinear parabolic equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• An energy equation for the weakly damped driven nonlinear Schrödinger equations and its application to their attractors
• Multichannel nonlinear scattering for nonintegrable equations
• Global strichartz estimates for nonthapping perturbations of the laplacian
• On Fourier coefficients and transforms of functions of two variables
• Maximal functions associated to filtrations
• Unnamed Item
• Unnamed Item