Bifurcation structure of dissipative solitons

DOI10.1016/j.physd.2006.12.008zbMath1148.34033OpenAlexW2152647360MaRDI QIDQ875463

N. E. Zubov

Publication date: 13 April 2007

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2006.12.008

zbMATH Keywords

invariant manifoldspattern formationlocalized structureshomoclinic and heteroclinic bifurcationsnonlinear optical cavitiesreversible dynamical systems

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Lasers, masers, optical bistability, nonlinear optics (78A60) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (12)

Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators ⋮ Optical crystals and light-bullets in Kerr resonators ⋮ Defect-mediated snaking: a new growth mechanism for localized structures ⋮ Bifurcation analysis to the Lugiato-Lefever equation in one space dimension ⋮ Localized Turing patterns in nonlinear optical cavities ⋮ Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure ⋮ Analysis of spatial patterns in a vegetation model ⋮ Complex spatial structures due to atomic coherence ⋮ Exponential asymptotics of localised patterns and snaking bifurcation diagrams ⋮ Homoclinic snaking: Structure and stability ⋮ On homoclinic snaking in optical systems ⋮ Guided Modes and Symmetry Breaking Supported by Localized Gain

Cites Work

• Cascades of reversible homoclinic orbits to a saddle-focus equilibrium
• Pattern formation in a passive Kerr cavity
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Subharmonic Branching in Reversible Systems
• Gluing unstable fronts and backs together can produce stable pulses
• A new approach to data storage using localized structures

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