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Cauchy problem for the generalized Davey-Stewartson systems in Besov spaces and some counterexamples
Ganshan Yang
Keywords:Davey-Stewartson systems; F-expansion method; multi-order exact solutions; Lam functions; Cauchy problem.
      In this paper, the Cauchy problem of the generalized ellipse-ellipse type Davey-Stewartson systems is discussed. When the dimension of space is greater than or equal to two, we get a unique global solution in Besov spaces by contraction mapping argument. By using the F-expansion method the exact periodic wave solutions for the generalized ellipse-ellipse type Davey-Stewartson systems are discussed, some counter examples are given over bounded domain. Some exact global smooth solutions are constructed for generalized ellipse-hyperbolic and hyperbolic-hyperbolic type Davey-Stewartson systems.