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Publisher’s description: 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 Schrödinger (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.
The articles of this volume will be reviewed individually.
Indexed articles:
Deift, Percy A., Three lectures on “Fifty years of KdV: an integrable system”, 3-38 [Zbl 1461.37070]
Gérard, Patrick, Wave turbulence and complete integrability, 39-93 [Zbl 1442.35419]
Saut, Jean-Claude, Benjamin-Ono and intermediate long wave equations: modeling, IST and PDE, 95-160 [Zbl 1442.35355]
Perry, Peter A., Inverse scattering and global well-posedness in one and two space dimensions, 161-252 [Zbl 1442.35429]
Dieng, Momar; McLaughlin, Kenneth D. T.-R.; Miller, Peter D., Dispersive asymptotics for linear and integrable equations by the \(\overline{\partial}\) steepest descent method, 253-291 [Zbl 1441.35047]
Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana, Instability of solitons in the 2D cubic Zakharov-Kuznetsov equation, 295-371 [Zbl 1440.35267]
Kappeler, Thomas; Topalov, Peter, On the nonexistence of local, gauge-invariant Birkhoff coordinates for the focusing NLS equation, 373-395 [Zbl 1447.35298]
Kwak, Chulkwang; Muñoz, Claudio, Extended decay properties for generalized BBM equation, 397-411 [Zbl 1442.35383]
Ibrahim, Slim, Ground state solutions of the complex Gross Pitaevskii equation, 413-432 [Zbl 1442.81067]
Mizumachi, Tetsu, The phase shift of line solitons for the KP-II equation, 433-495 [Zbl 1442.35396]
Pelinovsky, Dmitry E.; Saalmann, Aaron, Inverse scattering for the massive Thirring model, 497-528 [Zbl 1442.35362]