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On the Cauchy problem for the Kadomtsev-Petviashvili equation. (English) Zbl 0787.35086
The author gives a global result for the Cauchy problem of the Kadomtsev- Petviashvili equation. The solution is globally well-posed for initial data in \(L^ 2(\mathbb{R}^ 2/\mathbb{Z}^ 2)\). The result is obtained on extending a local result (obtained by applying a Picard fixed point argument) to a global one with the help of the \(L^ 2\)-conservation law.
The method is analogous to the one used for the Schrödinger and Korteweg-de Vries equations, and it is based on an analysis of multiple Fourier series.
Reviewer: L.Vazquez (Madrid)

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
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