Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 59, pp. 1-12.

Title: Unique continuation property for the 
       Kadomtsev-Petviashvili (KP-II) equation
       
Author: Mahendra Panthee (Tribhuvan University, Kirtipur, Nepal)

Abstract: 
 We generalize a method introduced by Bourgain in \cite{Borg} 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.
   
Submitted April 9, 2005. Published June 10, 2005.
Math Subject Classifications: 35Q35, 35Q53
Key Words: Dispersive equations; KP equation; unique continuation property;
           smooth solution; compact support.