  This work continues our studies of nonlinear evolution of a system of
wavepackets. We study a wave propagation governed by a nonlinear system of
hyperbolic PDE's with constant coefficients with the initial data being a
multi-wavepacket. By definition a general wavepacket has a well defined
principal wave vector, and, as we proved in previous works, the nonlinear
dynamics preserves systems of wavepackets and their principal wave vectors.
Here we study the nonlinear evolution of a special class of wavepackets, namely
particle-like wavepackets. A particle-like wavepacket is of a dual nature: on
one hand, it is a wave with a well defined principal wave vector, on the other
hand, it a particle in the sense that it can be assigned a well defined
position in the space. We prove that under the nonlinear evolution a generic
multi-particle wavepacket remains to be a multi-particle wavepacket with a high
accuracy, and every constituting single particle-like wavepacket not only
preserves its principal wave number but also it has a well-defined space
position evolving with a constant velocity which is its group velocity.
Remarkably the described properties hold though the involved single
particle-like wavepackets undergo nonlinear interactions and multiple
collisions in the space. We also prove that if principal wavevectors of
multi-particle wavepacket are generic, the result of nonlinear interactions
between different wavepackets is small and the approximate linear superposition
principle holds uniformly with respect to the initial spatial positions of
wavepackets.
