Kdv '95: Proceedings of the International Symposium Held in Amsterdam, the Netherlands, April 23-26, 1995, to Commemorate the C

ISBN-13: 9789401040112 / Angielski / Miękka / 2012 / 516 str.

Michiel Hazewinkel; Hans W. Capel; Eduard M. De Jager

Opis

Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase Korteweg-de Vries equation' in their title or abstract, and there are thousands more in other areas, such as biology, chemistry, electronics, geology, oceanology, meteorology, etc. And, of course, the KdV equation is only one of what are now called (Liouville) completely integrable systems. The KdV and its relatives continually turn up in situations when one wishes to incorporate nonlinear and dispersive effects into wave-type phenomena.
This centenary provides a unique occasion to survey as many different aspects of the KdV and related equations. The KdV equation has depth, subtlety, and a breadth of applications that make it a rarity deserving special attention and exposition.

Spis treści

Preface; E.M. de Jager. Part I: Invited Plenary Lectures. Integrability, Computation and Applications; M.J. Ablowitz, S. Chakravarty, B. M. Herbst. Applications of KdV; D.G. Crighton. Instructive History of the Quantum Inverse Scattering Method; L. Faddeev. Optical Solitons in Communications: From Integrability to Controllability; A. Hasegawa. Korteweg, de Vries, and Dutch Science at the Turn of the Century; A.J. Kox. Algebraic-Geometrical Methods in the Theory of Integrable Equations and Their Perturbations; I. Krichever. An ODE to PDE: Glories of the KdV Equation. An Appreciation of the Equation on its 100th Birthday! M.D. Kruskal. The Discrete Korteweg-de Vries Equation; F. Nijhoff, H. Capel. Coherent Structure Visiometrics: From the Soliton to HEC; N.J. Zabusky. Part II: Invited Contributions. The KPI Equation with Unconstrained Initial Data; M. Boiti, F. Pempinelli, A. Pogrebkov. Solitons and the Korteweg-de Vries Equation: Integrable Systems in 1834-1995; R.K. Bullough, P.J. Caudrey. Integrable Nonlinear Evolution Equations and Dynamical Systems in Multidimensions; F. Calgero. Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations; P.A. Clarkson, E.L. Mansfield. A KdV Equation in 2+1 dimensions: Painlevé Analysis, Solutions and Similarity Reductions; P.G. Estévez, S.B. Leble. The Korteweg-de Vries Equation and Beyond; A.S. Fokas. On the Background of Limit Pass for Korteweg-de Vries Equation as the Dispersion Vanishes; V.A. Galkin, V.V. Russkikh. On New Trace Formulae for Schrödinger Operators; F. Gesztesy, H. Holden. KdV Equations and Integrability Detectors; B. Grammaticos, V. Papageorgiou, A. Ramani. Generalized Self-Dual Yang-Mills Flows, ExplicitSolutions and Reductions; C.-H. Gu. Symbolic Software for Soliton Theory; W. Hereman, W. Zhuang. Solitons of Curvature; B.G. Konopelchenko. The Reductive Perturbation Method and the Korteweg&endash;de Vries Hierarchy; R.A. Kraenkel, J.G. Pereira, M.A. Manna. Darboux Transformations for Higher-Rank Kadomtsev&endash;Petviashvili and Krichever&endash;Novikov Equations; G.A. Latham, E. Previato. Moment Problem of Hamburger, Hierarchies of Integrable Systems, and the Positivity of Tau-Functions; Y. Nakamura, Y. Kodama. New Features of Soliton Dynamics in 2+1 Dimensions; F. Pempinelli. Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg&endash;de Vries Equation; A.Ye. Rednikov, M.G. Velarde, Yu.S. Ryazantsev, A.A. Nepomnyashchy, V.N. Kurdyumov. Recent Results on the Generalized Kadomtsev&endash;Petviashvili Equations; J.-C. Saut. An Explicit Expression for the Korteweg&endash;de Vries Hierarchy; R. Schimming. Evolving Solitons in Bubbly Flows; L. van Wijngaarden.