Seminar "Elliptic solutions to BKP equation and many-body systems" by Anton Zabrodin

Date

Wednesday, January 30, 2019 - 11:00 to 12:00

Location

C016, Lab1

Description

  • Date: Wednesday, January 30
  • Time: 11:00-12:00
  • Venue: C016, Lab1
  • Speaker: Anton Zabrodin (National Research University Higher School of Economics, Moscow)
  • Title: Elliptic solutions to BKP equation and many-body systems
  • Abstract:

We derive equations of motion for poles of double-periodic (elliptic) solutions to the B-version of the KP equation. The motivation is the well-known story about elliptic solutions of the usual KP equation, where the dynamics of poles is given by the Calogero-Moser many-body system with elliptic potential. 

The basic tool is the auxiliary linear problem for the wave function.

The result is a new many-body dynamical system with three-body interaction expressed through the Weierstrass elliptic function. This system does not admit Lax representation but, instead, it is equivalent to a sort of Manakov's triple equation with a spectral parameter. 

We also discuss integrals of motion which follow from the equation of the spectral curve and analyze analytic properties of the wave function on the spectral curve.

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