Nonlinear Dispersive Equations : Inverse Scattering and PDE Methods / by Christian Klein, Jean-Claude Saut.
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, fr...
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| Main Authors: | , |
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| Format: | Ebook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2021.
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| Edition: | First edition 2021. |
| Series: | Applied mathematical sciences (Springer-Verlag New York Inc.) ;
209. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | 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. |
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| Physical Description: | 1 online resource (xx, 580 pages 87 illus., 68 illus. in color). |
| ISBN: | 3030914267 9783030914264 3030914275 9783030914271 |
| ISSN: | 2196-968X ; |