Ankündigung Erscheint vsl. April 2022 Abbildung von Klein / Saut | Nonlinear Dispersive Equations | 1. Auflage | 2022 | 209 |

Klein / Saut

Nonlinear Dispersive Equations

Inverse Scattering and PDE Methods

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Buch. Hardcover

1st ed. 2022. 2022

xx, 574 S. 1 s/w-Abbildung, 86 Farbabbildungen, Bibliographien.

In englischer Sprache

Springer. ISBN 978-3-030-91426-4

Format (B x L): 15,5 x 23,5 cm

Das Werk ist Teil der Reihe: Applied Mathematical Sciences; 209


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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