A Priori Bounds and Global Bifurcation Results for Frequency Combs Modeled by the Lugiato--Lefever Equation

DOI10.1137/16M1066221zbMath1397.34069arXiv1603.02206OpenAlexW2963967116MaRDI QIDQ2967903

Rainer Mandel, Wolfgang Reichel

Publication date: 9 March 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.02206

zbMATH Keywords

bifurcationLugiato-Lefever equationCrandall-Rabinowitz theoremfrequency combs

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Bifurcation theory for ordinary differential equations (34C23) Physical optics (78A10)

Related Items (12)

Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides ⋮ Periodic waves of the Lugiato–Lefever equation at the onset of Turing instability ⋮ Linear modulational and subharmonic dynamics of spectrally stable Lugiato-Lefever periodic waves ⋮ On the Barashenkov-Bogdan-Zhanlav solitons and their stability ⋮ The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption ⋮ Nonlinear modulational dynamics of spectrally stable Lugiato-Lefever periodic waves ⋮ Global continua of solutions to the Lugiato-Lefever model for frequency combs obtained by two-mode pumping ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Dynamics of waves and patterns. Abstracts from the workshop held August 8--14, 2021 (hybrid meeting) ⋮ Soliton Solutions for the Lugiato–Lefever Equation by Analytical and Numerical Continuation Methods ⋮ On the Generation of Stable Kerr Frequency Combs in the Lugiato--Lefever Model of Periodic Optical Waveguides ⋮ Global secondary bifurcation, symmetry breaking and period-doubling

Uses Software

• Matlab
• AUTO

Cites Work

• Unnamed Item
• Bifurcation from a degenerate simple eigenvalue
• A simple criterion for transverse linear instability of nonlinear waves
• Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
• Bifurcation theory. An introduction with applications to partial differential equations
• Strang splitting for a semilinear Schrödinger equation with damping and forcing
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Bifurcation with a two-dimensional kernel
• Bifurcation at Double Characteristic Values

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