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

• 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.