Amanda Petcu, Department of Pure Mathematics, University of Waterloo
"Hamiltonian Structures for Evolution Equations Describing Pseudo-Spherical Surfaces"
The calculation of conservation laws for a differential equation has been a problem of interest for many researchers. The conservation laws that arise naturally from physics such as conservation of mass and momentum are but a drop in a bucket. This is why we are very interested in algorithms that could provide an infinite sequence of conservation laws for certain classes of evolution equations. This seminar will explore two classes of evolution equations for which there exist algorithms that create an infinite hierarchy of conservation laws for the equation. The first class are evolution equations that describe pseudo-spherical surfaces. The second class are evolution equations which admit a multi-Hamiltonian structure. Since these two classes of evolution equations share this property, the question of whether or not there exist evolution equations that describe pseudo-spherical surfaces and also admit a multi-Hamiltonian structure will be explored in the case of the KdV equation and another quintic evolution equation.