Nonlinear dynamical regimes of the generalized Kuramoto-Sivashinsky equation with various degrees of nonlinearity

The stabilizing effects of dispersion on the dynamics of the generalized Kuramoto equation with three different degrees of nonlinearity are considered. The second and third sections investigate the traveling wave reduction of the studied equation. The fourth section explores the changing dynamics of the generalized Kuramoto–Sivashinsky PDE by calculating its largest Lyapunov exponents over a range of values of the dispersion parameter.