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Nonlinear Dispersive Equations

Nonlinear Dispersive Equations

Inverse Scattering and PDE Methods

Christian Klein, Jean-Claude Saut

Springer
Collection: Applied Mathematical Sciences
Publication date : 2022-02-23

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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.

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About the book

Author

Christian Klein , Jean-Claude Saut

Imprint

Springer

Collection

Applied Mathematical Sciences

Publication date

2022-02-23

Pages

580 pages

Print ISBN

9783030914264

Language

English

Ebook informations

EAN PDF

9783030914271

Price

£129.50

Copy count 5

Print count 58

File size 21453 Ko

Informations accessibility

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About author(s)

Christian Klein

Jean-Claude Saut

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