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Titlebook: Lectures on Integrable Systems; Jens Hoppe Book 1992 Springer-Verlag Berlin Heidelberg 1992 Dynamische Systeme.Hamiltonian.Hamiltonian mec

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发表于 2025-3-21 17:27:26 | 显示全部楼层 |阅读模式
书目名称Lectures on Integrable Systems
编辑Jens Hoppe
视频video
丛书名称Lecture Notes in Physics Monographs
图书封面Titlebook: Lectures on Integrable Systems;  Jens Hoppe Book 1992 Springer-Verlag Berlin Heidelberg 1992 Dynamische Systeme.Hamiltonian.Hamiltonian mec
描述Mainly drawing on explicit examples, the author introducesthe reader to themost recent techniques to study finite andinfinite dynamical systems.Without any knowledge ofdifferential geometry or lie groups theory the student canfollow in a series of case studies the most recentdevelopments. r-matrices for Calogero-Moser systems andTodalattices are derived. Lax pairs for nontrivial infinitedimensionalsystems are constructed as limits of classicalmatrix algebras. The readerwill find explanations of theapproach to integrable field theories, to spectral transformmethods and to solitons. New methods are proposed, thushelping students not only to understand establishedtechniques but also to interest them in modern research ondynamical systems.
出版日期Book 1992
关键词Dynamische Systeme; Hamiltonian; Hamiltonian mechanics; Integrierbare Systeme; differential geometry; dyn
版次1
doihttps://doi.org/10.1007/978-3-540-47274-2
isbn_softcover978-3-662-13882-3
isbn_ebook978-3-540-47274-2Series ISSN 0940-7677
issn_series 0940-7677
copyrightSpringer-Verlag Berlin Heidelberg 1992
The information of publication is updating

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Solution of a Quantum Mechanical ,-Body Problem,total momentum operator . commutes with (3.1) (due to the potential . depending only on the differences of the particle coordinates) the eigenfunctions ψ of (3.1) may be chosen to be also eigenfunctions of .; let us restrict ourselves to functions satisfying
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,Integrable Systems and gl(∞),echanics to (quantum) field theory having many different aspects, and in concrete models various physical interpretations, we will choose a purely . point of view — as in the context of integrable systems this turns out to be rather useful (yielding, e.g., a large class of possibilities which would
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Integrable Field Theories from Poisson Algebras,Poisson-bracket {,} on some space of functions from a (compact) manifold to the field ℂ (or IR), e.g. . — which is . of the type (10.1) — there exists an additional . assotiative multiplication, which is the one implied when writing . ., e.g., and which is the ordinary multiplication of functions. C
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Generalized Garnier Systems and Membranes,here exists another type of non-linear interaction, which is rather special: the class of quartic potentials. In the finite dimensional case, FWM [.] used the Lax-representation of the non-linear Schrödinger model to generalize the original work of Garnier [.]. In a compact notation (and dropping a
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Zero Curvature Conditions on ,,, Trigonometrical and Universal Enveloping Algebras,ties involved a finite number of . and . dependent fields . .(.) (. = 1 ... .), that made up .. The constant matrix . was chosen diagonal, and the construction of the constants of motion relied on the possibility to ‘diagonalize’ . by means of a similarity transformation ., which required the soluti
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Spectral Transform and Solitons,mportant role since then. Curiously, it uses the formulation (and abstract solution) of a problem known from quantum mechanics, namely that of solving . for given .(.), which is supposed to be a smooth real function and to go to zero (sufficiently fast) as . → ± ∞.
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