Variational method for finding periodic orbits in a general flow.
The intriguing “Hopf’s last hope”— proposal for a theory of turbulence has significant physical meaning. The problem is how to describe chaotic/turbulent spatiotemporal patterns. Typical system exhibiting spatiotemporal chaos is the Kuramoto-Sivashinsky(KS for short) system. It is a prototype to model the development of turbulence in physical systems. The basic equation is ut = (u)x − uxx − vuxxxx. The project mainly studies the chaotic properties of the KuramotoSivashinsky system. The periodic solutions of the system are found by the Newton-Raphson method some other novel variational methods. They are discussed in  and .