Global well-posedness of partially periodic KP-I equation in the energy space and application |
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Authors: | Tristan Robert |
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Affiliation: | Université de Cergy-Pontoise, Laboratoire AGM, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France |
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Abstract: | In this article, we address the Cauchy problem for the KP-I equation for functions periodic in y. We prove global well-posedness of this problem for any data in the energy space . We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flow, as long as its speed is small enough. |
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Keywords: | Kadomtsev–Petviashvili equation Global well-posedness Orbital stability KdV line soliton |
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