  We establish a connection between the hyperbolic relativistic Calogero-Moser
systems and a class of soliton solutions to the Tzitzeica equation (aka the
Dodd-Bullough-Zhiber-Shabat-Mikhailov equation). In the 6N-dimensional phase
space $\Omega$ of the relativistic systems with 2N particles and $N$
antiparticles, there exists a 2N-dimensional Poincar\'e-invariant submanifold
$\Omega_P$ corresponding to $N$ free particles and $N$ bound
particle-antiparticle pairs in their ground state. The Tzitzeica $N$-soliton
tau-functions under consideration are real-valued, and obtained via the dual
Lax matrix evaluated in points of $\Omega_P$. This correspondence leads to a
picture of the soliton as a cluster of two particles and one antiparticle in
their lowest internal energy state.
