Instabilities and splitting of pulses in coupled Ginzburg-Landau equations

DOI10.1016/S0167-2789(01)00243-3zbMath0977.35021OpenAlexW2060918860MaRDI QIDQ5938412

Boris A. Malomed, Hidetsugu Sakaguchi

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)00243-3

zbMATH Keywords

mirror symmetryHopf bifurcationcascade of splitting of solitary-pulsessolitary-pulse solutions with a stable zero background

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Yang-Mills and other gauge theories in quantum field theory (81T13) Bifurcations in context of PDEs (35B32) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

Related Items (7)

Modulational instability in linearly coupled complex cubic-quintic Ginzburg-Landau equations ⋮ Stable solitons in coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities ⋮ Exact solutions in nonlinearly coupled cubic-quintic complex Ginzburg-Landau equations ⋮ Dromion-like structures and stability analysis in the variable coefficients complex Ginzburg-Landau equation ⋮ Noise-induced stabilization of bumps in systems with long-range spatial coupling ⋮ Solitary pulses in linearly coupled Ginzburg-Landau equations ⋮ Long-time behavior of solution for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities

Cites Work

• Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system
• Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations
• Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations
• Nonlinear Schrödinger equation including growth and damping
• Pattern formation outside of equilibrium
• On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance
• Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system

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