  We consider the Kadomtsev-Petviashvili (KP) equations posed on
$\mathbb{R}^2$. For both equations, we provide sequential in time asymptotic
descriptions of solutions, of arbitrarily large data, inside regions not
containing lumps or line solitons, and under minimal regularity assumptions.
The proof involves the introduction of two new virial identities adapted to the
KP dynamics, showing decay in large regions of space, especially in the KP-I
case, where no monotonicity property was previously known. Our results do not
require the use of the integrability of KP and are adaptable to well-posed
perturbations of KP.
