Nonlinear Dispersive Equations: Inverse Scattering and Pde Methods (Applied Mathematical Sciences #209) (Paperback)

Nonlinear Dispersive Equations: Inverse Scattering and Pde Methods (Applied Mathematical Sciences #209) By Christian Klein, Jean-Claude Saut Cover Image

Nonlinear Dispersive Equations: Inverse Scattering and Pde Methods (Applied Mathematical Sciences #209) (Paperback)

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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 andnon-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.


Product Details ISBN: 9783030914295
ISBN-10: 3030914291
Publisher: Springer
Publication Date: February 25th, 2023
Pages: 580
Language: English
Series: Applied Mathematical Sciences