In this work, we study the one-dimensional stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out o...

A robust approach for adjoint-based sensitivity analysis of chaotic dynamics based on unstable periodic orbits is proposed. We show that a careful reformulation of established variational techniques to such trajectories enables the sensitivity of time averages with respect to design parameters to be calculated exactly, regardless of the stability characteristics and length of the orbit. This ho...

We evaluate a method to describe subcritical transitions in systems with a finitewavelength instability (pattern forming systems) by means of a direct expansion in the amplitude of the linearly least stable mode. We apply the method to two model equations, a subcritical generalization of the Swift-Hohenberg equation and an extension of the Kuramoto-Sivashinsky equation. We assess the reliabilit...

We consider the numerical solution of nonlinear, dissipative partial differential equations using a pseudospectral method and the methodology of approximate inertial manifolds. Coarse and fine grids are employed, with a nonlinear mapping to relate the solutions computed on these grids. The approach is illustrated by consideration of the Kuramoto-Sivashinsky equation subject to periodic solution...

We study steady thin reaction fronts described by the Kuramoto-Sivashinsky equation that separates fluids of different densities. This system may lead to hydrodynamic instabilities as buoyancy forces interact with the propagating fronts in a two-dimensional slab. We use Darcy's law to describe the fluid motion in this geometry. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric...