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Titlebook: Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory; Peter E. Zhidkov Book 2001 Springer-Verlag Berlin Heidelberg 20

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发表于 2025-3-21 17:53:00 | 显示全部楼层 |阅读模式
书目名称Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory
编辑Peter E. Zhidkov
视频videohttp://file.papertrans.cn/541/540004/540004.mp4
概述Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory;  Peter E. Zhidkov Book 2001 Springer-Verlag Berlin Heidelberg 20
描述- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of ap
出版日期Book 2001
关键词Well-posedness; invariant measure; ordinary differential equation; stability; stationary solution; partia
版次1
doihttps://doi.org/10.1007/3-540-45276-1
isbn_softcover978-3-540-41833-7
isbn_ebook978-3-540-45276-8Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2001
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发表于 2025-3-22 00:10:23 | 显示全部楼层
Lecture Notes in Mathematicshttp://image.papertrans.cn/k/image/540004.jpg
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Evolutionary equations. Results on existence,In this chapter we consider several results on the well-posedness of initial-value problems for the KdVE and NLSE that are used in the next sections. In Additional remarks to this chapter, we mention additional literature on this subject. Now we prove the result, generally well-known, which is intensively exploited further.
发表于 2025-3-22 09:00:43 | 显示全部楼层
Stationary problems,As we have already noted in the Introduction, the substitution of the general representation for standing waves .(.) = . .φ(.), ω ∈ ., into the NLSE leads to the stationary equation ..
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978-3-540-41833-7Springer-Verlag Berlin Heidelberg 2001
发表于 2025-3-22 17:18:27 | 显示全部楼层
Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory978-3-540-45276-8Series ISSN 0075-8434 Series E-ISSN 1617-9692
发表于 2025-3-22 23:12:15 | 显示全部楼层
https://doi.org/10.1007/3-540-45276-1Well-posedness; invariant measure; ordinary differential equation; stability; stationary solution; partia
发表于 2025-3-23 05:16:54 | 显示全部楼层
Invariant measures,h measures in the infinite-dimensional case when a dynamical system is generated by a nonlinear partial differential equation. In this chapter, we illustrate these investigations for the NLSE and KdVE with our two results. Some other literature on this subject is indicated in Additional remarks.
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