# Transverse bifurcation of viscous slow MHD shocks

## TL;DR

This paper combines analytical and numerical Evans function methods to analyze the stability and transverse bifurcation of multi-D viscous and inviscid slow MHD shocks, revealing a preference for nonplanar traveling wave solutions.

## Contribution

It presents the first multi-D numerical Evans function study for viscous MHD shocks and demonstrates the agreement between viscous and inviscid stability transitions.

## Key findings

- Nonplanar traveling waves are typical in slow Lax MHD shocks.
- Viscous and inviscid stability transitions align.
- First multi-D numerical Evans function analysis for viscous MHD.

## 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.