ANISOTROPIC KURAMOTO-SIVASHINSKY EQUATION FOR SURFACE GROWTH AND EROSION

We study the anisotropic two-dimensional Kuramoto-Sivashinsky equation partial derivative(t)h = [-partial derivative(x)(2) - alpha partial derivative(y)(2) - (partial derivative(x)(2) + partial derivative(y)(2))(2)] h + 1/2 [(partial derivative(x)h)(2) + beta(partial derivative(y)h)(2)], With real parameters alpha, beta, which arises, e.g., in sputter erosion and epitaxial growth on vicinal surfaces. The nonlinearities stabilize the linear instability, leading to a state of bounded spatiotemporal chaos, only if beta > min(0, alpha). Otherwise the equation exhibits two symmetry-related families of exponentially growing solutions for which the nonlinearities cancel. The competition between the two families gives rise to a coarsening pattern of rippled domains.