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Lecture 1 Analysis of Riemann - Hilbert problems, some nuts and bolts, and applications to the detailed description of solitonic interactions for the KdV equation and MKdV equation.

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

This talk is intended to be an introduction to the analysis of Riemann-Hilbert problems in applications to the study of solitonic interactions. We will start with a brief summary of direct scattering theory aimed at the Riemann-Hilbert problem formulation of the inverse scattering problem.  Then we will develop the classic asymptotic calculation of the phase shift in the interaction between two solitons, explained via an analysis of the meromorphic Riemann-Hilbert problem characterizing this solution. Following that, time permitting, we will cut to the chase scene, and see how to compute the interaction of a single soliton with a regular soliton gas.  In the negative time that remains after that, we will discuss how to characterize more general configurations of solitonic gasses via a Riemann-Hilbert formulation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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