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Nonlinear dispersive equationsinvers...

Klein, Christian.

Nonlinear dispersive equationsinverse scattering and pde methods /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlinear dispersive equationsby Christian Klein, Jean-Claude Saut.
其他題名:	inverse scattering and pde methods /
作者:	Klein, Christian.
其他作者:	Saut, J.-C.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	1 online resource (xx, 580 p.) :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Differential equations, Partial.
電子資源:	https://doi.org/10.1007/978-3-030-91427-1
ISBN:	9783030914271$q(electronic bk.)

Nonlinear dispersive equationsinverse scattering and pde methods /
Klein, Christian.

Nonlinear dispersive equationsinverse scattering and pde methods /[electronic resource] :by Christian Klein, Jean-Claude Saut. - Cham :Springer International Publishing :2021. - 1 online resource (xx, 580 p.) :ill. (some col.), digital ;24 cm. - Applied mathematical sciences,v. 2092196-968X ;. - Applied mathematical sciences ;v.176..

Acronyms -- Glossary -- 1 General Introduction -- 2 Generalities and Basic Facts -- 3 Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE -- 4 Davey-Stewartson and Related Systems -- 5 Kadomtsev-Petviashvili and Related Equations -- 6 Novikov-Veselov and Derivative Nonlinear Schrodinger Equations -- Index.

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.

ISBN: 9783030914271$q(electronic bk.)

Standard No.: 10.1007/978-3-030-91427-1doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377 / K54 2021

Dewey Class. No.: 515.353

Nonlinear dispersive equationsinverse scattering and pde methods /
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520 $a 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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