This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing NLS equation, the massive Thirring model, and the BBM equation as dispersive PDE in one space dimension, as well as the KP-II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions.  The meeting coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the one-dimensional cubic nonlinear Schrodinger (NLS) equation, the derivative NLS equation and, in two dimensions, the Davey-Stewartson, Kadomtsev-Petviashvili and the Novikov-Veselov equations. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing and used as a powerful analytical tool to study global well-posedness and elucidate long-time asymptotic behavior of the solutions, including dispersion, soliton solutions, and semiclassical limits.weiterlesen