This repository contains the notebook with symbolic computations in SAGE for the paper "Transverse bifurcation of viscous slow MHD shocks", by Blake Barker, Rafael Monteiro, and Kevin Zumbrun. The code is not intended to be optimized, and in several parts (believe it or not) we chose clarity to the detriment of efficiency. The preprint can be found here.
The paper has been published as
It can be cited as
@article{BARKER2021132857,
title = {Transverse bifurcation of viscous slow MHD shocks},
journal = {Physica D: Nonlinear Phenomena},
volume = {420},
pages = {132857},
year = {2021},
issn = {0167-2789},
doi = {https://doi.org/10.1016/j.physd.2021.132857},
url = {https://www.sciencedirect.com/science/article/pii/S0167278921000154},
author = {Blake Barker and Rafael Monteiro and Kevin Zumbrun},
keywords = {Magnetohydrodynamics, Bifurcation, Stability of shock waves (inviscid and viscous), Lopatinsky condition, Multi-D Evans function numerical computations},
abstract = {We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of Zumbrun and Serre.}
}
You can download and unzip this repository from GitHub, either interactively, or by entering
git clone https://github.com/rafael-a-monteiro-math/Transverse-bifurcation-of-viscous-slow-MHD-shocks.git