Soliton Solutions for the Lugiato–Lefever Equation by Analytical and Numerical Continuation Methods

DOI10.1007/978-3-030-47174-3_11zbMath1466.34040OpenAlexW3091369297MaRDI QIDQ4964113

Janina Gärtner, Wolfgang Reichel

Publication date: 24 February 2021

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-47174-3_11

zbMATH Keywords

implicit function theoremsoliton solutionLugiato-Lefever equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Applications of operator theory to differential and integral equations (47N20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

Global continua of solutions to the Lugiato-Lefever model for frequency combs obtained by two-mode pumping

Uses Software

• pde2path

Cites Work

• Unnamed Item
• Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
• Strang splitting for a semilinear Schrödinger equation with damping and forcing
• Global secondary bifurcation, symmetry breaking and period-doubling
• A Priori Bounds and Global Bifurcation Results for Frequency Combs Modeled by the Lugiato--Lefever Equation
• Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides
• Periodic waves of the Lugiato–Lefever equation at the onset of Turing instability

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