Applied Mathematical Sciences: Nonlinear Dispersive Equations
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This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin–Ono, Davey–Stewartson, and Kadomtsev–Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena.
By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Autoren-Profil
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.
