# Gain of Regularity for the KP-I Equation - Mathematics > Analysis of PDEs

Abstract: In this paper we study the smoothness properties of solutions to the KP-Iequation. We show that the equation-s dispersive nature leads to a gain inregularity for the solution. In particular, if the initial data $\phi$possesses certain regularity and sufficient decay as $x \to \infty$, then thesolution $ut$ will be smoother than $\phi$ for $0 < t \leq T$ where $T$ isthe existence time of the solution.

Author: Julie Levandosky, Mauricio Sepulveda DIM, Octavio Vera

Source: https://arxiv.org/