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Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Hardcover, 1st ed. 2019): Peter D. Miller, Peter A.... Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Hardcover, 1st ed. 2019)
Peter D. Miller, Peter A. Perry, Jean-Claude Saut, Catherine Sulem
R3,830 Discovery Miles 38 300 Ships in 10 - 15 working days

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.

Integrable Systems and Applications - Proceedings of a Workshop Held at Oleron, France, June 20-24, 1988 (Paperback, Softcover... Integrable Systems and Applications - Proceedings of a Workshop Held at Oleron, France, June 20-24, 1988 (Paperback, Softcover reprint of the original 1st ed. 1989)
Mikhael Balabane, Pierre Lochak, Catherine Sulem
R1,591 Discovery Miles 15 910 Ships in 10 - 15 working days

In this volume nonlinear systems related to integrable systems are studied. Lectures cover such topics as the application of integrable systems to the description of natural phenomena, the elaboration of perturbation theories, and the statistical mechanics of ensembles of objects obeying integrable equations. The more physical lectures center largely around the three paradigmatic equations: Korteweg de Vries, Sine-Gordon and Nonlinear Schroedinger, especially the latter. These have long been of great mathematical interest, and also exhibit a "universality" which places them among the most frequently encountered integrable equations in the description of physical systems. Tidal waves, optical fibers and laser beams are among the topics discussed. Lectures are also devoted to multidimensional solitons, integrability of Hamiltonian systems of ODEs and dissipative systems of PDEs.

The Nonlinear Schroedinger Equation - Self-Focusing and Wave Collapse (Paperback, Softcover reprint of the original 1st ed.... The Nonlinear Schroedinger Equation - Self-Focusing and Wave Collapse (Paperback, Softcover reprint of the original 1st ed. 1999)
Catherine Sulem, Pierre-Louis Sulem
R4,509 Discovery Miles 45 090 Ships in 10 - 15 working days

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

The Nonlinear Schroedinger Equation - Self-Focusing and Wave Collapse (Hardcover, 1999 ed.): Catherine Sulem, Pierre-Louis Sulem The Nonlinear Schroedinger Equation - Self-Focusing and Wave Collapse (Hardcover, 1999 ed.)
Catherine Sulem, Pierre-Louis Sulem
R4,715 Discovery Miles 47 150 Ships in 10 - 15 working days

This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Paperback, 1st ed. 2019): Peter D. Miller, Peter A.... Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Paperback, 1st ed. 2019)
Peter D. Miller, Peter A. Perry, Jean-Claude Saut, Catherine Sulem
R3,798 Discovery Miles 37 980 Ships in 10 - 15 working days

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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