Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation
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We generalize a method introduced by Bourgain in  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
(ut + uxxx + uux)x + uyy = 0, (x, y) ∈ ℝ2, t ∈ ℝ,
is supported compactly in a nontrivial time interval then it vanishes identically.
CitationPanthee, M. (2005). Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation. Electronic Journal of Differential Equations, 2005(59), pp. 1-12.
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