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Derivation of Davey-Stewartson and its Lump Soliton Solutions

Analysis, Dynamics, and Applications Seminar

Derivation of Davey-Stewartson and its Lump Soliton Solutions
Series: Analysis, Dynamics, and Applications Seminar
Location: Hybrid: Math 402/Online
Presenter: Ruby Abrams, Program in Applied Mathematics, University of Arizona

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)