This directory contains the source code that generates the results presented here. The first 3 modules are as follow and contain the results discussed in Part 1 of the dissertation:
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Fourier Series: contains code for a
FourierSeriesobject and operations. -
Pulse Solution: contains code for a
PulseSolutionobject. This approximates the pulse solution to the Swift-Hohenberg equation using a Fourier series and Newton's method. -
Conjugate Points: contains code for a
ConjugatePointsobject. This computes the conjugate points associated to the pulse solution.
The following modules contain code that accompanies Part 2 of the dissertation.
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Bistable Bundles: contains code to compute the resonant and non-resonant vector bundles of the bistable equation discussed in Chapter 11.2.
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Invariant Manifolds: contains code to compute the invariant stable and unstable manifolds for the Swift-Hohenberg equation. This directory also contains a computer assisted proof of their existence. This is discussed in Chapter 9.1.
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L minus: contains code to compute the bound on
$L_-$ discussed in Chapters 8.1 and 10.2. -
Pseudo Arclength Continuation: contains code to compute branches of pulse solutions for the 1 D Swift-Hohenberg equation. This was exploratory work and is not included in the dissertation.
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Pulse Validation: contains code to compute a stationary pulse solution of the Swift-Hohenberg equation and a computer assisted proof of its existence. This is discussed in Chapter 9.
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Sequence Space: contains helper functions for operations in sequence space.
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Swift-Hohenberg Bundles: contains code to compute the resonant and non-resonant solutions of the Swift-Hohenberg equation as discussed in Chapter 11.3. This directory is self-contained.
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Vector Field: contains helper functions for expressing the Swift-Hohenberg equation, its vector field, and linearization about the origin.