From solitons to many-body systems

@article{BenZvi2003FromST,
  title={From solitons to many-body systems},
  author={David D. Ben-Zvi and T. Nevins},
  journal={Pure and Applied Mathematics Quarterly},
  year={2003},
  volume={4},
  pages={319-361}
}
We present a bridge between the KP soliton equations and the Calogero–Moser many-body systems through noncommutative algebraic geometry. The Calogero-Moser systems have a natural geometric interpretation as flows on spaces of spectral curves on a ruled surface. We explain how the meromorphic solutions of the KP hierarchy have an interpretation via a noncommutative ruled surface. Namely, we identify KP Lax operators with vector bundles on quantized cotangent spaces (formulated technically in… Expand
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