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Colin Thomson (UNC-CH), GMA Seminar
October 3, 2016 @ 4:00 pm - 5:00 pm
Title: Applications of the biHamiltonian structure of the Korteweg-de Vries equation
Abstract: Hamiltonian mechanics (along with its complement, Lagrangian mechanics) is a common formulation of classical dynamics. After reviewing the geometric structure of finite-dimensional Hamiltonian systems, we generalize to Hamiltonian partial differential equations, and show that the Korteweg-de Vries (KdV) equation for waves in shallow water has two distinct, but compatible, Hamiltonian structures. These independent structures may be used to establish two amazing facts about the KdV equation: there is an infinite sequence of conserved quantities and the equation can be solved exactly despite its nonlinearity. We conclude by applying the exact solution to multi-soliton dynamics.