Compute stability exponents for Kuramoto–Sivashinsky periodic states and test zeta predictions

Evaluate the stability exponents of a representative set of unstable periodic states of the Kuramoto–Sivashinsky equation (or another spatially one-dimensional PDE) and assess the accuracy of the predictions obtained from the spatiotemporal zeta function.

Background

A key ingredient in the spatiotemporal zeta function is the stability exponent (Hill determinant per unit spacetime volume) associated with each prime periodic state. For PDEs, such quantities have not yet been systematically computed within this framework.

Carrying out these computations for Kuramoto–Sivashinsky would provide an empirical test of the zeta-function formalism in continuous systems and benchmark its predictive power.