Universität Bielefeld

Freezing Method -- Decompose and Freeze Method -- Comsol Multiphysics

SFB 701 (Logo)
SFB 701
Fakultät für Mathematik
English version

Konferenzen

Freezing Relative Equilibria in Equivariant First-Order Evolution Equations (with Comsol Multiphysics 5.2)

1.1 Traveling waves in reaction diffusion systems
1.2 Freezing method for traveling waves
1.3 Numerical approximation of traveling waves via freezing method
1.4 Spectra and eigenfunctions of traveling waves
1.4.1 Point spectrum of traveling waves on the imaginary axis
1.4.2 Essential spectrum of traveling waves
2.1 Oscillating waves in reaction diffusion systems
2.2 Freezing method for oscillating waves
2.3 Numerical approximation of oscillating waves via freezing method
2.4 Spectra and eigenfunctions of oscillating waves
2.4.1 Point spectrum of oscillating waves on the imaginary axis
2.4.2 Essential spectrum of localized oscillating waves
3.1 Rotating waves in reaction diffusion systems
3.2 Freezing method for rotating waves
3.3 Numerical approximation of rotating waves via freezing method
4. Freezing Waves with Several Symmetries in Reaction Diffusion Systems
5. Freezing Multistructures (Multifronts, Multipulses and Multisolitons) and Wave Interactions in Reaction Diffusion Systems
6. Further coherent structures in Reaction Diffusion Systems

Freezing Relative Equilibria in Equivariant Second-Order Evolution Equations (with Comsol Multiphysics 5.2)

7.1 Traveling waves in systems of damped wave equations
7.2 Freezing method for traveling waves
7.3 Numerical approximation of traveling waves via freezing method
7.4 Spectra and eigenfunctions of traveling waves
7.4.1 Point spectrum of traveling waves on the imaginary axis
7.4.2 Essential spectrum of traveling waves
8. Freezing Rotating Waves in Damped Wave Equations
8.1 Rotating waves in systems of damped wave equations
8.2 Freezing method for rotating waves
8.3 Numerical approximation of rotating waves via freezing method

The model library of the examples below is summerized in the following file For the implementation of the results below we suggest the following Comsol tutorial Some further tutorials created by the older version Comsol 3.5a can be found here.

Freezing Relative Equilibria in Equivariant First-Order Evolution Equations (with Comsol Multiphysics 5.1 and 5.2)

1. Freezing Traveling Waves in Reaction Diffusion Equations

Equation Space Wave Phenomena Traveling wave Space-Time Profile Space-Time Velocities Spectrum Eigenfunction Files
Fisher's equation 1D traveling front mph
Nagumo equation 1D traveling front model.mph
figure_movie.m
nonfrozen.flv
frozen.flv
Quintic Nagumo equation 1D traveling front model.mph
figure_movie.m
nonfrozen.flv
frozen.flv
FitzHugh-Nagumo system 1D traveling front


mph
FitzHugh-Nagumo system 1D traveling pulse


mph
Barkley model 1D traveling pulse


mph

2. Freezing Oscillating Waves in Reaction Diffusion Equations

Equation Space Wave Phenomena Oscillating wave Space-Time Profile Space-Time Velocities Spectrum Eigenfunction Files
Schrödinger equation 1D oscillating pulse


mph
Gross-Pitaevskii equation 1D oscillating pulse


mph
cubic-quintic complex Ginzburg-Landau equation 1D oscillating pulse


mph

3. Freezing Rotating Waves in Reaction Diffusion Systems

Equation Space Wave Phenomena 3D-View Space-Time Profile Space-Time Velocities Spectrum Eigenfunction Files
cubic-quintic complex Ginzburg-Landau equation 2D spinning soliton, dissipative soliton, rotating soliton

mph
cubic-quintic complex Ginzburg-Landau equation 2D rotating spiral wave


mph
Lambda-omega system 2D rotating spiral wave mph
Barkley model 2D rotating spiral wave mph
cubic-quintic complex Ginzburg-Landau equation 3D spinning soliton, dissipative soliton, rotating soliton mph
mph
Lambda-omega system 3D scroll wave, scroll ring

4. Freezing Waves with Several Symmetries in Reaction Diffusion Systems

Equation Space Wave Phenomena Wave Phenomena Space-Time Profile Space-Time Velocities Spectrum Eigenfunction Files
Schrödinger equation 1D traveling oscillating pulse



mph
cubic-quintic complex Ginzburg-Landau equation 1D traveling oscillating front



mph

5. Freezing Multistructures (Multifronts, Multipulses and Multisolitons) and Wave Interactions in Reaction Diffusion Systems

Equation Space Wave Phenomena Wave Phenomena Space-Time Profile Space-Time Velocities, Positions Spectrum Eigenfunction Files
Nagumo equation 1D Traveling 2-front (traveling multifront, repelling fronts)


mph
Nagumo equation 1D Traveling 2-front (collision, colliding fronts)


mph
quintic Nagumo equation 1D Traveling 2-front (traveling multifront)

mph
quintic Nagumo equation 1D Traveling 2-front (collision)

mph
quintic Nagumo equation 1D Traveling 3-front (traveling multifront)
quintic Nagumo equation 1D Traveling 4-front (traveling multifront)
quintic Nagumo equation 1D Traveling 4-front (collision)
FitzHugh-Nagumo system 1D Traveling 2-pulse (traveling multipulse)
cubic-quintic complex Ginzburg-Landau equation 1D Oscillating 2-pulse (oscillating multipulse)
cubic-quintic complex Ginzburg-Landau equation 1D Oscillating pulse and traveling oscillating front
cubic-quintic complex Ginzburg-Landau equation 1D Traveling oscillating 2-front (traveling oscillating multifront)
cubic-quintic complex Ginzburg-Landau equation 2D Spinning 2-soliton (rotating multisoliton)
cubic-quintic complex Ginzburg-Landau equation 2D Spinning 3-soliton (rotating multisoliton)

6. Further coherent structures in Reaction Diffusion Systems

Equation Space Wave Phenomena Wave Phenomena Space-Time Profile Space-Time Velocities Spectrum Eigenfunction Files
cubic-quintic complex Ginzburg-Landau equation 1D pulsating soliton


mph
cubic-quintic complex Ginzburg-Landau equation 1D creeping soliton


mph

Freezing Relative Equilibria in Equivariant Second-Order Evolution Equations (with Comsol Multiphysics 5.1 and 5.2)

7. Freezing Traveling Waves in Damped Wave Equations

Equation Space Wave Phenomena Traveling wave Space-Time Profile Space-Time Velocity, Acceleration Spectrum Eigenfunction Files
Damped Fisher's equation 1D traveling front
Damped Nagumo equation 1D traveling front mph
Damped quintic Nagumo equation 1D traveling front mph
Damped FitzHugh-Nagumo system 1D traveling front


mph
Damped FitzHugh-Nagumo system 1D traveling pulse mph
Damped Barkley model 1D traveling pulse

8. Freezing Rotating Waves in Damped Wave Equations

Equation Space Wave Phenomena 3D-View Space-Time Profile Space-Time Velocities, Accelerations Spectrum Eigenfunction Files
damped cubic-quintic complex Ginzburg-Landau equation 2D spinning soliton, dissipative soliton, rotating soliton

Literature

 
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27. February 2017