Algebra Seminar
Thomas Creutzig, Edmonton/Erlangen
Representation theory of affine VOAs
4:00PM, Zoom (please email achirvas@buffalo.edu)
I will give an overview on the state of the art in this area.
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #1
4:00PM
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #2
4:00PM
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #3
4:00PM
Colloquium
Dr Willy Hereman, Colorado School of Mines
Symbolic computation of solitary wavesolutions and solitons through homogenization of degree
4:00PM, Mathematics Building room 250
A simplified version of Hirota's method for thecomputation of solitary waves and solitons of nonlinear PDEs will be presented.The approach requires a change of dependent variable so that the transformedPDE is homogenous of degree in the new variable.
The resulting homogenous PDE does not have tobe quadratic and the method still applies if its bilinear form is not known.Solitons are then computed using a perturbation scheme involving linear andnonlinear operators. For soliton equations the scheme terminates after a finitenumber of steps. To illustrate the approach, solitons are computed for a classof fifth-order KdV equations due to Lax, Sawada-Kotera, and Kaup-Kupershmidt.
Homogenization of degree also allows one tofind solitary wave solutions of nonlinear PDEs that are not completelyintegrable. Examples include the Fisher and FitzHugh-Nagumo equations, and acombined KdV-Burgers equation. When applied to a wave equation with a cubicsource term, the method leads to a `bi-soliton' solution which describes thecoalescence of two wavefronts.
The method is largely algorithmic andimplemented in Mathematica. A demonstration of the software packagePDESolitonsSolutions will be given.
Applied Math Seminar
Willy Hereman, Colorado School of Mines
Symbolic computation of conservation laws of nonlinear partial differential equations.
3:00PM, Math 122