Derivation of Davey-Stewartson and its Lump Soliton Solutions
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Davey-Stewartson Equation (DSE) is a 2+1 dimensional generalization of the Nonlinear Schrodinger equation (NSE). In this talk, I present a derivation of DSE from a Lax Pair, demonstrating that it is an integrable system. Then, I give an overview of the Inverse Scattering Transform to show how the Gelfand-Levitan-Marchenko (GLM) arises. This is the starting point of the new Dressing Method, which is used to directly construct unknown potentials of the Dirac Operator. Lastly, I'll present solutions of the DS equations and argue that these solutions correspond to the Lax Pair I started with (not obvious).
Place: Hybrid, Math, 402 and Zoom: https://arizona.zoom.us/j/81150211038 Password: “arizona” (all lower case)