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Explore a lecture on the mathematical theory of solitons and soliton gas delivered by Tamara Grava from the University of Bristol as part of Harvard CMSA's program on Classical, quantum, and probabilistic integrable systems. Discover the properties of solitons as localized traveling wave solutions of nonlinear dispersive equations, with a focus on their elastic interactions in integrable systems. Learn about the behavior of multiple solitons for the Korteweg de Vries equation as their number approaches infinity (soliton gas), and understand how a tracer soliton interacts with this gas. The presentation demonstrates that the average velocity of the tracer soliton follows the Zakharov-El kinetic equations and presents a central limit theorem for the difference between random N-soliton solutions and their limiting soliton gas for values bounded by log(N).
