Tzitzeica solitons vs. relativistic Calogero-Moser 3-body clusters
نویسندگان
چکیده
We establish a connection between the hyperbolic relativistic Calogero-Moser systems and a class of soliton solutions to the Tzitzeica equation (aka the DoddBullough-Zhiber-Shabat-Mikhailov equation). In the 6N -dimensional phase space Ω of the relativistic systems with 2N particles and N antiparticles, there exists a 2N dimensional Poincaré-invariant submanifold ΩP 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 ΩP . This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.
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