19-23 June 2023
Faculty of Physics, University of Warsaw
Europe/Warsaw timezone
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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

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