Applied Mathematical Sciences: Nonlinear Dispersive Equations

Christian Klein · Jean-Claude Saut

Feb 2022 · Applied Mathematical Sciences Toleo la #209 · Springer Nature

Kitabu pepe

580

Kurasa

Ukadiriaji na maoni hayajahakikishwa Pata Maelezo Zaidi

Kuhusu kitabu pepe hiki

Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose–Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems.
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.

Kuhusu mwandishi

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.

Kadiria kitabu pepe hiki

Tupe maoni yako.

Kusoma maelezo

Simu mahiri na kompyuta vibao

Sakinisha programu ya Vitabu vya Google Play kwa ajili ya Android na iPad au iPhone. Itasawazishwa kiotomatiki kwenye akaunti yako na kukuruhusu usome vitabu mtandaoni au nje ya mtandao popote ulipo.

Kompyuta za kupakata na kompyuta

Unaweza kusikiliza vitabu vilivyonunuliwa kwenye Google Play wakati unatumia kivinjari cha kompyuta yako.

Visomaji pepe na vifaa vingine

Ili usome kwenye vifaa vya wino pepe kama vile visomaji vya vitabu pepe vya Kobo, utahitaji kupakua faili kisha ulihamishie kwenye kifaa chako. Fuatilia maagizo ya kina ya Kituo cha Usaidizi ili uhamishe faili kwenye visomaji vya vitabu pepe vinavyotumika.

Ripoti maudhui yanayokiuka sera