Traveling hole solutions of the complex Ginzburg-Landau equation: A review

DOI10.1016/S0167-2789(01)00174-9zbMath0977.35023OpenAlexW1982580135MaRDI QIDQ5940213

Joceline C. Lega

Publication date: 6 January 2002

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00174-9

zbMATH Keywords

one-parameter family of solutionstraveling holes and their stability

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (12)

The phase structure of grain boundaries ⋮ Stationary modulated-amplitude waves in the 1D complex Ginzburg-Landau equation ⋮ Transition to spatiotemporal chaos via stationary branching shocks and holes ⋮ All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations ⋮ Optical solitons with complex Ginzburg-Landau equation for two nonlinear forms using \(F\)-expansion ⋮ Asymptotic behavior of stochastic discrete complex Ginzburg--Landau equations ⋮ Dark soliton dynamics under the complex Ginzburg-Landau equation ⋮ Stability of nonlinear waves: pointwise estimates ⋮ The world of the complex Ginzburg-Landau equation ⋮ Generation of periodic travelling waves in cyclic populations by hostile boundaries ⋮ Unfolding spatiotemporal dynamics through symmetry reduction based on orbit topology ⋮ Non-existence of elliptic travelling wave solutions of the complex Ginzburg--Landau equation

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