Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
Springer-Verlag New York Inc.
978-1-4939-9805-0 (ISBN)
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.
Fifty years of KdV: an integrable system (P. Deift).- Wave turbulence and complete integrability (P. Gerard).- Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST, and PDE (J.-C. Saut).- Inverse scattering and global well-posedness in one and two dimensions (P. Perry).- Dispersive asymptotics for linear and integrable equations by the d-bar steepest descent method (M. Dieng, K. McLaughin, P. Miller).- Instability of solutions in the 2d Zakharov-Kuznetzov equation (L. Farah, J. Holmer, S. Roudenko).- On the nonexistence of local, gauge-invariant Birkhoff coordinates for focussing NLS equation (T. Kappeler, P. Topalov).- Extended decay properties for generalized BBM equation (C. Kwok, C. Munoz).- Ground state solutions of the complex Gross-Pitaevskii equation (T. Mizumachi).- Inverse scattering for the massive Thirring model (D. Pelinovsky, A. Saalman).- Anomolous (rogue) waves in nature, their recurrence, and the nonlinear Schrodinger model (P. Santini, P. Grinevich).
Erscheinungsdatum | 29.11.2019 |
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Reihe/Serie | Fields Institute Communications ; 83 |
Zusatzinfo | 5 Illustrations, color; 9 Illustrations, black and white; X, 528 p. 14 illus., 5 illus. in color. |
Verlagsort | New York |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Schlagworte | asymptotic stability • completely integrable method • Davey-Stewartson equation • Kadomtsev-Petviashvili equation • Nekhoroshev stability • Novikov-Veselov equation • Riemann- Hilbert problems • Sobolev norms • soliton resolution conjecture |
ISBN-10 | 1-4939-9805-6 / 1493998056 |
ISBN-13 | 978-1-4939-9805-0 / 9781493998050 |
Zustand | Neuware |
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