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Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Paperback, 1st ed. 2019)
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Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Paperback, 1st ed. 2019)
Series: Fields Institute Communications, 83
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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 nonlinear Schroedinger (NLS) equation, the massive
Thirring model, and the Benjamin-Bona-Mahoney equation as
dispersive PDE in one space dimension, as well as the
Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov
equation, and the Gross-Pitaevskii equation as dispersive PDE in
two space dimensions. The Focus Program 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 cubic NLS equation, and
the derivative NLS equation in one space dimension and the
Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov
equations in two space dimensions. These models have been
extensively studied and, in some cases, the inverse scattering
theory has been put on rigorous footing. It has been used as a
powerful analytical tool to study global well-posedness and
elucidate asymptotic behavior of the solutions, including
dispersion, soliton resolution, and semiclassical limits.
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