An asymptotic expansion for Bloch functions on Riemann surfaces of infinite genus and almost periodicity of the Kadomtsev-Petviashvili flow (Q1973261)
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scientific article; zbMATH DE number 1436909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An asymptotic expansion for Bloch functions on Riemann surfaces of infinite genus and almost periodicity of the Kadomtsev-Petviashvili flow |
scientific article; zbMATH DE number 1436909 |
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An asymptotic expansion for Bloch functions on Riemann surfaces of infinite genus and almost periodicity of the Kadomtsev-Petviashvili flow (English)
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16 January 2001
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Asymptotic expansion of Bloch is applied to get the solution of the Kadomtsev-Petviashvili equation with \(C^{10}\) real periodic initial data. The block functions are parametrized by the spectral variety of a heat equation with an external potential. To get the spectral variety the Riemann-Roch theorem for Riemann surfaces of infinite genus is used. KP flow is represented by a one-parameter-subgroup in the real part of the Jacobi variety of this Riemann surface. Compactness of the real part of the Jacobi variety yields the almost periodicity of the KP-I flow.
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Kadomtsev-Petviashvili flow
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Jacobi variety
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Riemann-Roch theorem
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infinite genus Riemann surfaces
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