  A dynamics of spatially extended particles, hidden in the dynamics of line
solitons in more than one space dimension, is revealed through conservation
laws obeyed by the single-soliton solution. These are functions of the solution
of a nonlinear evolution equation and its derivatives, which vanish for a
single-soliton solution. They map multi-line-soliton solutions into systems of
vertices - spatially extended structures, localized around the
soliton-collision regions. In more than one space dimension, vertices move in
space, emulating the dynamics of spatially extended particles. Examples are
provided through the analysis of several soliton solutions of the
Kadomtsev-Petviashvili (KP) equation in (1+2)-dimensions. The solution with one
collision region is mapped onto a single vertex, which moves at a constant
velocity, preserving its spatial structure, thereby emulating a free particle.
In solutions with several collision regions, each region is mapped onto a
vertex. When vertices are well separated, they also emulate free particles.
They move in space, coalesce upon collision, and then split up. The total
particle linear momentum is conserved through the collision in all solutions
studied. However, depending on the soliton solution, particle masses and the
total kinetic energy may change.
