Extracting the Additive Phase Shifts from the 2-soliton solution of the MKDV
This oral comprehensive exam talk in the field of integrable systems accomplishes the following: 1) deriving the focusing MKDV equation from a Lax Pair, 2) applying the Dressing Method to solve the Lax Pair, 3) solving the focusing MKDV equation for 1- and 2-soliton solutions, and 4) extracting the additive phase shifts from the 2-soliton solution. The talk concludes on future work for the topic of my dissertation: A Kinetic Theory of MKDV Solitons. Instead of describing a many-soliton solution (e.g. 10^8 solitons) analytically, physicists are interested in looking at a statistical description of "soliton gases", effectively describing an "integrable turbulence". It all depends on the additive phase shift.