Geodesic
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation
Electronic journal of differential equations, Tome 2005 (2005)
We generalize a method introduced by Bourgain in citeBorg based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation

$ (u_t+u_{xxx}+uu_{x})_{x} +u_{yy}=0, \quad (x, y) \in \mathbb{R}^2, \;t\in\mathbb{R}, $

is supported compactly in a nontrivial time interval then it vanishes identically.
Classification : 35Q35, 35Q53
Keywords: dispersive equations, KP equation, unique continuation property, smooth solution, compact support 
@article{EJDE_2005__2005__a19,
     author = {Panthee,  Mahendra},
     title = {Unique continuation property for the {Kadomtsev-Petviashvili} {(KP-II)} equation},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1080.35125},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a19/}
}
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Panthee,  Mahendra. Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a19/