Local Attractors in One Boundary-Value Problem for the Kuramoto–Sivashinsky Equation

A boundary-value problem for the generalized Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions is considered in the paper. The analysis of stability of spatially homogeneous equilibrium states is given and local bifurcations are studied at the changes of their stability. When solving the problem, we use the method of invariant manifolds in combination with the theory of normal forms. The asymptotic formulas are found for bifurcating solutions.