KdV ’95 : Proceedings of the International Symposium Held in Amsterdam, The Netherlands, April 23–26, 1995, to Commemorate the Centennial of the Publication of the Equation by and Named After Korteweg and De Vries

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. Front Matter....Pages i-2 Front Matter....Pages 3-3 Integrability, Computation and Applications....Pages 5-37 Applications of KdV....Pages 39-67 Instructive History of the Quantum Inverse Scattering Method....Pages 69-84 Optical Solitons in Communications: From Integrability To Controllability....Pages 85-90 Korteweg, de Vries, and Dutch Science at the Turn of the Century....Pages 91-92 Algebraic—Geometrical Methods in the Theory of Integrable Equations and Their Perturbations....Pages 93-125 An ODE to a PDE: Glories of the KdV Equation. An Appreciation of the Equation on Its 100th Birthday!....Pages 127-132 The Discrete Korteweg—de Vries Equation....Pages 133-158 Coherent Structure Visiometrics:From the Soliton to HEC....Pages 159-172 Front Matter....Pages 173-173 The KPI Equation with Unconstrained Initial Data....Pages 175-192 Solitons and the Korteweg—de Vries Equation: Integrable Systems in 1834–1995....Pages 193-228 Integrable Nonlinear Evolution Equations and Dynamical Systems in Multidimensions....Pages 229-244 Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations....Pages 245-276 A KdV Equation in 2 + 1 Dimensions: Painlevé Analysis, Solutions and Similarity Reductions....Pages 277-294 The Korteweg—de Vries Equation and Beyond....Pages 295-305 On the Background of Limit Pass for Korteweg—de Vries Equation as the Dispersion Vanishes....Pages 307-314 On New Trace Formulae for Schrödinger Operators....Pages 315-333 KdV Equations and Integrability Detectors....Pages 335-348 Generalized Self-Dual Yang—Mills Flows, Explicit Solutions and Reductions....Pages 349-360 Symbolic Software for Soliton Theory....Pages 361-378 Front Matter....Pages 173-173 Solitons of Curvature....Pages 379-387 The Reductive Perturbation Method and the Korteweg—de Vries Hierarchy....Pages 389-403 Darboux Transformations for Higher-Rank Kadomtsev—Petviashvili and Krichever—Novikov Equations....Pages 405-433 Moment Problem of Hamburger, Hierarchies of Integrable Systems, and the Positivity of Tau-Functions....Pages 435-443 New Features of Soliton Dynamics in 2 + 1 Dimensions....Pages 445-455 Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg—de Vries Equation....Pages 457-475 Recent Results on the Generalized Kadomtsev—Petviashvili Equations....Pages 477-487 An Explicit Expression for the Korteweg—de Vries Hierarchy....Pages 489-505 Evolving Solitons in Bubbly Flows....Pages 507-516