19-23 June 2023
Faculty of Physics, University of Warsaw
Europe/Warsaw timezone
Degree growth of some lattice equations defined on a 3x3 stencil
Presented by Prof. Jarmo HIETARINTA
on
22 Jun 2023
from
12:00
to
12:30
Content
We study the growth of complexity, or degree growth, of one-component
lattice equations defined on a 3x3 stencil. The 2x2 case was discussed
in a previous talk by T. Mase. The equations studied here include two
7-point equations in Hirota bilinear form as well as 9-point
Boussinesq equations of regular, modified and Schwarzian type.
The initial values are given on a staircase or on a corner configuration and
depend linearly or rationally on a special variable x, and we count
the degree in x of the iterates. Known integrable cases have linear
growth if only one initial values contains x, and quadratic growth if
all initial values contain x. Even a small deformation of an
integrable equation changes the degree growth to become exponential,
because the deformation will change factorization properties and
thereby prevent cancellations. The simplest case in which only one initial
value contains x is sufficient to differentiate between integrable
and non-integrable equations.
Place
Location: Faculty of Physics, University of Warsaw
Address: Pasteura 5, Warsaw
Room: Lecture hall: 0.06