Bifurcation to traveling waves in the cubic–quintic complex Ginzburg–Landau equation

DOI10.1142/S0219530514500419zbMath1316.35029MaRDI QIDQ5253867

Philip Strzelecki, Jung Ho Park

Publication date: 5 June 2015

Published in: Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hopf bifurcationgeneralized Ginzburg-Landau equationquasi-periodic amplitude traveling waves

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Traveling wave solutions (35C07) Ginzburg-Landau equations (35Q56)

Cites Work

• Bifurcation and stability of the generalized complex Ginzburg-Landau equation
• Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation
• Periodic and quasi-periodic solutions of degenerate modulation equations
• Traveling waves in the complex Ginzburg-Landau equation
• Numerical simulations of periodic travelling waves to a generalized Ginzburg-Landau equation
• The world of the complex Ginzburg-Landau equation
• Bounded solutions of the nonlinear parabolic amplitude equation for plane Poiseuille flow
• Low-dimensional behaviour in the complex Ginzburg-Landau equation
• Dynamic Bifurcation of the Ginzburg--Landau Equation
• Distant side-walls cause slow amplitude modulation of cellular convection
• Finite bandwidth, finite amplitude convection
• A non-linear instability theory for a wave system in plane Poiseuille flow
• Non-linear wave-number interaction in near-critical two-dimensional flows

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