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Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution |
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| Authors: | L Molinet J C Saut N Tzvetkov |
| Institution: | (1) L.A.G.A., Institut Galilée, Université Paris 13, 93430 Villetaneuse, France;(2) UMR de Mathématiques, Université de Paris-Sud, Bat. 425, 91405 Orsay Cedex, France;(3) Département de Mathématiques, Université Lille I, 59 655 Villeneuve d’Ascq Cedex, France |
| Abstract: | We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely). |
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