Abstract

In this paper we study the smoothness properties of solutions to the KP-I equation. We show that the equation's dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data φ{symbol} possesses certain regularity and sufficient decay as x → ∞, then the solution u (t) will be smoother than φ{symbol} for 0 < t ≤ T where T is the existence time of the solution. © 2008 Elsevier Inc. All rights reserved.