Other Nonlinear Dispersive Models
In this chapter we will discuss local and global well-posedness for some dispersive models arising in different physical situations. Our goal is to present some relevant results associated to the equations we will treat 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 finally in Section 9.5 we will examine the Zakharov systems. Finally, in Section 9.6 we will briefly discuss the inverse scattering method and well-posedness results regarding higher order KdV equations.
KeywordsWeighted Sobolev Space Strichartz Estimate Schwartz Class Zakharov System Small Amplitude Solution
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