عنوان

A spectral theory for simply periodic solutions of the Sinh-Gordon equation /

شابک

303001276X

شابک

9783030012762

شابک اشتباه

3030012751

شابک اشتباه

9783030012755

عنوان اصلي

A spectral theory for simply periodic solutions of the Sinh-Gordon equation /

نام عام مواد

[Book]

نام نخستين پديدآور

Sebastian Klein.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

[2018]

نام خاص و کميت اثر

1 online resource

عنوان فروست

Lecture notes in mathematics ;

مشخصه جلد

2229

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Part I Spectral Data. -- Introduction. -- Minimal Immersions into the 3-Sphere and the Sinh-Gordon Equation. -- Spectral Data for Simply Periodic Solutions of the Sinh-Gordon Equation. -- Part II The Asymptotic Behavior of the Spectral Data. -- The Vacuum Solution. -- The Basic Asymptotic of the Monodromy. -- Basic Behavior of the Spectral Data. -- The Fourier Asymptotic of the Monodromy. -- The Consequences of the Fourier Asymptotic for the Spectral Data. -- Part III The Inverse Problem for the Monodromy. -- Asymptotic Spaces of Holomorphic Functions. -- Interpolating Holomorphic Functions. -- Final Description of the Asymptotic of the Monodromy. -- Non-special Divisors and the Inverse Problem for the Monodromy. -- Part IV The Inverse Problem for Periodic Potentials (Cauchy Data). -- Divisors of Finite Type. -- Darboux Coordinates for the Space of Potentials. -- The Inverse Problem for Cauchy Data Along the Real Line. -- Part V The Jacobi Variety of the Spectral Curve. -- Estimate of Certain Integrals. -- Asymptotic Behavior of 1-Forms on the Spectral Curve. -- Construction of the Jacobi Variety for the Spectral Curve. -- The Jacobi Variety and Translations of the Potential. -- Asymptotics of Spectral Data for Potentials on a Horizontal Strip. -- Perspectives.

بدون عنوان

0

متن يادداشت

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030012762

عنوان

Spectral theory for simply periodic solutions of the Sinh-Gordon equation.

شماره استاندارد بين المللي کتاب و موسيقي

9783030012755

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential equations.

موضوع مستند نشده

Functional analysis.

موضوع مستند نشده

Functions of complex variables.

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential equations.

موضوع مستند نشده

Functional analysis.

موضوع مستند نشده

Functions of complex variables.

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

MAT007000

موضوع مستند نشده

PBKJ

موضوع مستند نشده

PBKJ

شماره

ويراست

شماره رده

شماره رده

نشانه اثر

نشانه اثر

مستند نام اشخاص تاييد نشده

Klein, Sebastian

تاريخ عمليات

20200823072815.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y