# Balanced flux formulations for multidimensional Evans function computations for viscous shocks

## TL;DR

This paper introduces a new coordinate formulation for computing the Evans function in multidimensional viscous shock stability analysis, extending the benefits of integrated coordinates from 1D to higher dimensions.

## Contribution

It proposes a novel coordinate choice that enables effective Evans function computations in multidimensional settings, where integrated coordinates are not available.

## Key findings

- New coordinate formulation facilitates Evans function computation in multiple dimensions
- Extends benefits of integrated coordinates from 1D to multidimensional cases
- Enhances stability analysis of viscous shock profiles in higher dimensions

## Abstract

The Evans function is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is typical to compute the Evans function using Goodman's integrated coordinates [G1]; this device facilitates the search for zeros of the Evans function by winding number arguments. Although integrated coordinates are not available in the multidimensional case, we show here that there is a choice of coordinates which gives similar advantages.