Methods of solving Nonlinear PDE
When
Integrable Systems make up a set of measure 0 in the space of all dynamical systems, yet (countable) infinitely many important equations in physics can be shown to be integrable including NLS, KDV, Sine-Gordon (SG), Davey-Stewartson (DS), Self Dual Yang Mills (SDYM), among others. These PDEs are canonical examples of infinite dimensional Hamiltonian systems that have natural action-angle coordinates. A brief history will be given to show how problem formulations are derived in the form of the AKNS system and deriving Lax's equation. I will then demonstrate how to derive MKDV, KP-1 (and perhaps DS) and how to solve them using the Dressing Method, Hirota's Bilinear Method and the Gramian form for the KP-1 equation. Time permitting, I will give a demonstration of a visualization software of KP-1 solutions.
Place: Math, 402 and Zoom: https://arizona.zoom.us/j/82075792519 Password: 150721