TL;DR
This paper demonstrates the stability of particle pair configurations in the elliptic Calogero-Moser model under a specific Hamiltonian flow, linking it to elliptic solutions of the KP equation.
Contribution
It establishes the stability of paired particle configurations and connects their dynamics to elliptic solutions of the KP equation.
Findings
Pair configurations are stable under the third Hamiltonian flow.
Equations of motion for pairs match those of elliptic KP solutions.
Provides a link between Calogero-Moser particles and integrable PDE solutions.
Abstract
We show that the configuration in the phase space of the elliptic Calogero-Moser model when particles stick together in pairs is stable under the third Hamiltonian flow of the model. The equations of motion for the pairs coincide with the equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev-Petviashvili equation.
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