Infinite Dimensional Geometric Singular Perturbation Theory for the Maxwell--Bloch Equations

DOI10.1137/S0036141000360458zbMath1077.78015OpenAlexW2006587802MaRDI QIDQ2753548

Govind K. Menon, György Haller

Publication date: 11 November 2001

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036141000360458

zbMATH Keywords

invariant manifoldsMaxwell-Bloch equationsgeometric singular perturbation theory

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) Lasers, masers, optical bistability, nonlinear optics (78A60) Infinite-dimensional dissipative dynamical systems (37L99)

Related Items (8)

Slow manifolds for infinite-dimensional evolution equations ⋮ Invariant Manifolds in the Second-Order Maxwell–Bloch Equations ⋮ Local Theory for Spatio-Temporal Canards and Delayed Bifurcations ⋮ Exact model reduction by a slow-fast decomposition of nonlinear mechanical systems ⋮ Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach ⋮ Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions ⋮ Inverse scattering transform for two-level systems with nonzero background ⋮ Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations

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