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.
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
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.
test: contains some unit tests to check the code.
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 (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.