Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation

Abstract

We generalize a method introduced by Bourgain in [2] 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.