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Swift-Hohenberg-stability

This code is written by Hannah Pieper and accompanies the paper The Maslov Index, degenerate crossings, and the stability of pulse solutions to the Swift-Hohenberg equation by Margaret Beck, Jonathan Jaquette and Hannah Pieper.

Subdirectories

results: Contains the numerics presented in Section 5 of the paper. Run main.m.

source: Contains the source code that generates the results. This code is organized into 3 modules:

  • Fourier Series: contains code for a FourierSeries object and operations.
  • Pulse Solution: contains code for a PulseSolution object. This approximates the pulse solution to the Swift-Hohenberg equation using a Fourier series and Newton's method.
  • Conjugate Points: contains code for a ConjugatePoints object. This computes the conjugate points associated to the pulse solution.

test: contains some unit tests to check the code.

Software Requirements

This code requires Matlab and the Optimization Toolbox Add-On. If you try to run the main script or live script and you do not have the Optimization Toolbox, the Matlab editor will prompt you to install it.

Copyright and License

Copyright (C) 2024 M Beck, J Jaquette, and H Pieper.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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This repository contains the code accompanying [PAPER].

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