Christian Klein is Professor of mathematical physics at the Université de Bourgogne in Dijon, France, and a senior member of the Institut Universitaire de France. He works on nonlinear dispersive PDEs, numerical approaches, integrable systems, applied algebraic geometry and general relativity. His main interest is the numerical study of zones of rapid oscillations in the solutions to nonlinear dispersive equations, so-called dispersive shock waves, and a loss of regularity, a so-called blow-up of the solutions.Jean-Claude Saut is Emeritus Professor in the Laboratoire de Mathématiques of the Université Paris-Saclay. He works on the analysis of nonlinear dispersive equations and on their rigorous derivation as asymptotic models of general systems. His recent works concern a general class of Boussinesq systems, the analysis of weakly dispersive perturbations of the Burgers equation, and higher order models in the modulation regime of water waves.

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• Acronyms.- Glossary.- 1 General Introduction.- 2 Generalities and Basic Facts.- 3 Benjamin–Ono and Intermediate Long Wave Equations: Modeling, IST and PDE.- 4 Davey–Stewartson and Related Systems.- 5 Kadomtsev–Petviashvili and Related Equations.- 6 Novikov–Veselov and Derivative Nonlinear Schrödinger Equations.- Index.

Christian Klein is Professor of mathematical physics at the Université de Bourgogne in Dijon, France, and a senior member of the Institut Universitaire de France. He works on nonlinear dispersive PDEs, numerical approaches, integrable systems, applied algebraic geometry and general relativity. His main interest is the numerical study of zones of rapid oscillations in the solutions to nonlinear dispersive equations, so-called dispersive shock waves, and a loss of regularity, a so-called blow-up of the solutions.Jean-Claude Saut is Emeritus Professor in the Laboratoire de Mathématiques of the Université Paris-Saclay. He works on the analysis of nonlinear dispersive equations and on their rigorous derivation as asymptotic models of general systems. His recent works concern a general class of Boussinesq systems, the analysis of weakly dispersive perturbations of the Burgers equation, and higher order models in the modulation regime of water waves.

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• Acronyms.- Glossary.- 1 General Introduction.- 2 Generalities and Basic Facts.- 3 Benjamin–Ono and Intermediate Long Wave Equations: Modeling, IST and PDE.- 4 Davey–Stewartson and Related Systems.- 5 Kadomtsev–Petviashvili and Related Equations.- 6 Novikov–Veselov and Derivative Nonlinear Schrödinger Equations.- Index.

Christian Klein is Professor of mathematical physics at the Université de Bourgogne in Dijon, France, and a senior member of the Institut Universitaire de France. He works on nonlinear dispersive PDEs, numerical approaches, integrable systems, applied algebraic geometry and general relativity. His main interest is the numerical study of zones of rapid oscillations in the solutions to nonlinear dispersive equations, so-called dispersive shock waves, and a loss of regularity, a so-called blow-up of the solutions.Jean-Claude Saut is Emeritus Professor in the Laboratoire de Mathématiques of the Université Paris-Saclay. He works on the analysis of nonlinear dispersive equations and on their rigorous derivation as asymptotic models of general systems. His recent works concern a general class of Boussinesq systems, the analysis of weakly dispersive perturbations of the Burgers equation, and higher order models in the modulation regime of water waves.

Select Guide Rating

• Acronyms.- Glossary.- 1 General Introduction.- 2 Generalities and Basic Facts.- 3 Benjamin–Ono and Intermediate Long Wave Equations: Modeling, IST and PDE.- 4 Davey–Stewartson and Related Systems.- 5 Kadomtsev–Petviashvili and Related Equations.- 6 Novikov–Veselov and Derivative Nonlinear Schrödinger Equations.- Index.