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Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity
Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity
Organizers
Speaker
Da-Jun Zhang
Time
Venue
A3-2a-302
Online
Zoom 638 227 8222
(BIMSA)
Abstract
In the first part we will have a brief review of the lattice Boussinesq-type equations. In the second part we establish solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains a Cauchy kernel on the torus, is obtained by introducing the so-called ‘elliptic cube root of unity’.
References:
[1] Jarmo Hietarinta, Da-jun Zhang, Discrete Boussinesq-type equations, arXiv:2012.00495.
[2] Frank W. Nijhoff, Ying-ying Sun, Da-jun Zhang, Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity, Communications in Mathematical Physics, 399(2) (2003) 599-650.