Newton-Krylov continuation of amplitude-modulated rotating waves in sheared annular electroconvection.

We present an approach for studying the primary, secondary, and tertiary flow transitions in sheared annular electroconvection. In particular, we describe a Newton-Krylov method based on time integration for the computation of rotating waves and amplitude-modulated rotating waves, and for the continuation of these flows as a parameter of the system is varied. The method exploits the rotational nature of the flows and requires only a time-stepping code of the model differential equations, i.