Spatial structure of time-periodic solutions of the Ginzburg-Landau equation

DOI10.1016/0167-2789(86)90114-4zbMath0618.35003OpenAlexW2020411560MaRDI QIDQ1822265

Philip J. Holmes

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0167-2789(86)90114-4

zbMATH Keywords

nonlinear Schrödinger equationheteroclinic orbitscomplex Ginzburg-Landau equationintegrable limitspatially chaotic solutionsspatially decaying (homoclinic) solutionsspatially periodic and quasiperiodic solutions

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (25)

Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation ⋮ Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation ⋮ Bifurcations of plane wave (CW) solutions in the complex cubic--quintic Ginzburg--Landau equation ⋮ The complex cubic--quintic Ginzburg--Landau equation: Hopf bifurcations yielding traveling waves ⋮ Spatiotemporal structure of pulsating solitons in the cubic-quintic Ginzburg-Landau equation: A novel variational formulation ⋮ The Ginzburg–Landau equation for interfacial instabilities ⋮ Instability of quasiperiodic solutions of the Ginzburg–Landau equation ⋮ Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines ⋮ Numerical continuation of invariant solutions of the complex Ginzburg-Landau equation ⋮ Slow time-periodic solutions of the Ginzburg-Landau equation ⋮ Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2)-symmetry ⋮ Periodic and quasi-periodic solutions of degenerate modulation equations ⋮ A novel variational approach to pulsating solitons in the cubic-quintic Ginzburg-Landau equation ⋮ Time-periodic Ginzburg-Landau equations for one dimensional patterns with large wave length ⋮ The perturbed cubic Schrödinger equation: Selection mechanism, resonant limits, and spatial chaos ⋮ Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrödinger equations ⋮ Solutions of the Ginzburg-Landau Equation of Interest in Shear Flow Transition ⋮ Traveling wavetrains in the complex cubic-quintic Ginzburg-Landau equation ⋮ Breaking the hidden symmetry in the Ginzburg-Landau equation ⋮ Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation ⋮ Snake solitons in the cubic-quintic Ginzburg-Landau equation ⋮ Bifurcations and competing coherent structures in the cubic-quintic Ginzburg--Landau equation. I: Plane wave (CW) solutions ⋮ On the validity of the Ginzburg-Landau equation ⋮ Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders ⋮ Traveling waves in the complex Ginzburg-Landau equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the existence of separatrix loops in four-dimensional systems similar to the integrable Hamiltonian systems
• Periodic nonlinear waves on a half-line
• Periodic solutions of the Ginzburg-Landau equation
• Reduction of symplectic manifolds with symmetry
• Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
• Dynamics of Perturbed Wavetrain Solutions to the Ginzburg-Landau Equation
• Instabilities of the Ginzburg-Landau equation: periodic solutions
• Instabilities of the Ginzburg-Landau equation. II. Secondary bifurcation
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
• On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance

This page was built for publication: Spatial structure of time-periodic solutions of the Ginzburg-Landau equation