Global well-posedness for the KP-II equation on the background of a non-localized solution
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 5, p. 653-676
Motivated by transverse stability issues, we address the time evolution under the KP-II flow of perturbations of a solution which does not decay in all directions, for instance the KdV-line soliton. We study two different types of perturbations: perturbations that are square integrable in ×𝕋 and perturbations that are square integrable in 2 . In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.
@article{AIHPC_2011__28_5_653_0,
     author = {Molinet, Luc and Saut, Jean-Claude and Tzvetkov, Nikolay},
     title = {Global well-posedness for the KP-II equation on the background of a non-localized solution},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {5},
     year = {2011},
     pages = {653-676},
     doi = {10.1016/j.anihpc.2011.04.004},
     zbl = {1279.35079},
     mrnumber = {2838395},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_5_653_0}
}
Molinet, Luc; Saut, Jean-Claude; Tzvetkov, Nikolay. Global well-posedness for the KP-II equation on the background of a non-localized solution. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 5, pp. 653-676. doi : 10.1016/j.anihpc.2011.04.004. http://www.numdam.org/item/AIHPC_2011__28_5_653_0/

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