  The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of
infinite-dimensional integrable systems, which describes nonlinear ion acoustic
waves in two-dimensional space. This remarkably ordered system resides on a
singular submanifold (leaf) embedded in a larger phase space of more general
ion acoustic waves (low-frequency electrostatic perturbations). The KP
hierarchy is characterized not only by small amplitudes but also by
irrotational (zero-vorticity) velocity fields. In fact, the KP equation is
derived by eliminating vorticity at every order of the reductive perturbation.
Here we modify the scaling of the velocity field so as to introduce a vortex
term. The newly derived system of equations consists of a generalized
three-dimensional KP equation and a two-dimensional vortex equation. The former
describes `scattering' of vortex-free waves by ambient vortexes that are
determined by the latter. We say that the vortexes are `ambient' because they
do not receive reciprocal reactions from the waves (i.e., the vortex equation
is independent of the wave fields). This model describes a minimal departure
from the integrable KP system. By the Painlev\'e test, we delineate how the
vorticity term violates integrability, bringing about an essential
three-dimensionality to the solutions. By numerical simulation, we show how the
solitons are scattered by vortexes and become chaotic.
