Other Nonlinear Dispersive Models
In this chapter, we will discuss local and global well-posedness for some nonlinear dispersive models arising in different physical situations. Our goal is to present some relevant results associated to the equations to be contemplated here and it is by no means an exhaustive study of each of them. In Section 9.1 we will treat the Davey–Stewartson systems. The Ishimori equations will be considered in Section 9.2. The Kadomtsev–Petviashvili (KP) equations will be discussed in Section 9.3. The Benjamin–Ono equation will be studied in Section 9.4 and in Section 9.5 we will be examine the Zakharov systems. Finally, in Section 9.6 we will briefly review the inverse scattering method for the KdV equation and well-posedness results regarding higher order KdV equations.