The Kuramoto–Sivashinsky Equation (Part 3)

I’ve been getting a lot of help from Steve Huntsman and also Cheyne Weis, who is a physics grad student at the University of Chicago. You can see a lot, but far from all, of Steve’s work as comments on part 1. Here are some things Cheyne has been doing.

Cheyne started out working with the ‘derivative form’ of the Kuramoto–Sivashinsky equation, meaning this:

and he soon noticed what Steve made clear in the image above: the ‘stripes’ in solutions of this equation aren’t ‘bumps’ (regions wher...