Darboux Transformations in Integrable Systems : Theory and their Applications to Geometry

*- pocketboek*

2010, ISBN: 9048167884

[EAN: 9789048167883], Neubuch, [SC: 0.0], [PU: Springer Netherlands], MINKOWSKI SPACE; DIFFERENTIAL EQUATIONS; GEOMETRY; INVERSE SCATTERING THEORY; TWO-DIMENSIONAL MANIFOLDS, Druck auf Anfrage Neuware - GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e ective methods ofgetting explicit solutions of nonlinear partial di erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi erentialequationsappearinmanyscienti cpr- lems. Getting explicit solutions is usually a di cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method,B acklund transformation etc. The inverse scattering method is based on the spectral theory of ordinary di erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate. The B ac klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di erential equations. Some complicated nonlinear superposition formula arise to substitute the superposition principlein linear science. 320 pp. Englisch, Books

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Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Mathematical Physics Studies)

*- gebruikt boek*

ISBN: 9048167884

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method, B] acklund transformation etc.. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate. The B] ac ] klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science. math,mathematics,science and math Mathematics, Springer

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ISBN: 9789048167883

Paperback, [PU: Springer], GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method,B.. acklund transformation etc. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate. The B.. ac .. klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science., Differential Calculus & Equations, Differential & Riemannian Geometry, Mathematical Physics

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Darboux Transformations in Integrable Systems : Theory and their Applications to Geometry

*- pocketboek*

2010, ISBN: 9048167884

[EAN: 9789048167883], Neubuch, [PU: Springer Netherlands], DARBOUXTRANSFORMATIONS; MINKOWSKISPACE; DIFFERENTIALEQUATIONS; DIFFERENTIALGEOMETRY; INTEGRABLESYSTEMS; INVERSESCATTERINGTHEORY; SCATTERINGTHEORY; TWO-DIMENSIONALMANIFOLDS, Druck auf Anfrage Neuware - The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry.This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics. 320 pp. Englisch, Books

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Darboux Transformations in Integrable Systems ab 112.49 EURO Theory and their Applications to Geometry Mathematical Physics Studies. Softcover reprint of hardcover 1st ed. 2005 Medien > Bücher

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# Darboux Transformations in Integrable Systems : Theory and their Applications to Geometry* - pocketboek*

2010, ISBN: 9048167884

[EAN: 9789048167883], Neubuch, [SC: 0.0], [PU: Springer Netherlands], MINKOWSKI SPACE; DIFFERENTIAL EQUATIONS; GEOMETRY; INVERSE SCATTERING THEORY; TWO-DIMENSIONAL MANIFOLDS, Druck auf An… Meer...

## Gu, Chaohao; Hu, Anning; Zhou, Zixiang:

Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Mathematical Physics Studies)*- gebruikt boek*

ISBN: 9048167884

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, soli… Meer...

## ISBN: 9789048167883

Paperback, [PU: Springer], GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such a… Meer...

Darboux Transformations in Integrable Systems : Theory and their Applications to Geometry

*- pocketboek*

2010, ISBN: 9048167884

[EAN: 9789048167883], Neubuch, [PU: Springer Netherlands], DARBOUXTRANSFORMATIONS; MINKOWSKISPACE; DIFFERENTIALEQUATIONS; DIFFERENTIALGEOMETRY; INTEGRABLESYSTEMS; INVERSESCATTERINGTHEORY;… Meer...

2005, ISBN: 9048167884

gebonden uitgave

Darboux Transformations in Integrable Systems ab 112.49 EURO Theory and their Applications to Geometry Mathematical Physics Studies. Softcover reprint of hardcover 1st ed. 2005 Medien > B… Meer...

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** Gedetalleerde informatie over het boek. - Darboux Transformations in Integrable Systems**

EAN (ISBN-13): 9789048167883

ISBN (ISBN-10): 9048167884

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pocket book

Verschijningsjaar: 2010

Uitgever: Springer-Verlag GmbH

320 Bladzijden

Gewicht: 0,512 kg

Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2011-02-12T01:01:25+01:00 (Amsterdam)

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ISBN/EAN: 9789048167883

ISBN - alternatieve schrijfwijzen:

90-481-6788-4, 978-90-481-6788-3

### Gegevens van de uitgever

Auteur: Chaohao Gu; Anning Hu; Zixiang Zhou

Titel: Mathematical Physics Studies; Darboux Transformations in Integrable Systems - Theory and their Applications to Geometry

Uitgeverij: Springer; Springer Netherland

308 Bladzijden

Verschijningsjaar: 2010-10-28

Dordrecht; NL

Gedrukt / Gemaakt in

Gewicht: 0,514 kg

Taal: Engels

119,99 € (DE)

123,35 € (AT)

132,50 CHF (CH)

POD

BC; Previously published in hardcover; Hardcover, Softcover / Physik, Astronomie/Allgemeines, Lexika; Mathematische Physik; Verstehen; Darboux transformations; Minkowski space; differential equations; differential geometry; integrable systems; inverse scattering theory; scattering theory; two-dimensional manifolds; B; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Differential Geometry; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Differential Geometry; Physics and Astronomy; Mathematische Physik; Differentielle und Riemannsche Geometrie; BB

Preface.- 1. 1+1 Dimensional Integrable Systems.- 1.1 KdV equation, MKdV equation and their Darboux transformations. 1.1.1 Original Darboux transformation. 1.1.2 Darboux transformation for KdV equation. 1.1.3 Darboux transformation for MKdV equation. 1.1.4 Examples: single and double soliton solutions. 1.1.5 Relation between Darboux transformations for KdV equation and MKdV equation. 1.2 AKNS system. 1.2.1 2 × 2 AKNS system. 1.2.2 N × N AKNS system. 1.3 Darboux transformation. 1.3.1 Darboux transformation for AKNS system. 1.3.2 Invariance of equations under Darboux transformations. 1.3.3 Darboux transformations of higher degree and the theorem of permutability. 1.3.4 More results on the Darboux matrices of degree one. 1.4 KdV hierarchy, MKdV-SG hierarchy, NLS hierarchy and AKNS system with u(N) reduction. 1.4.1 KdV hierarchy. 1.4.2 MKdV-SG hierarchy. 1.4.3 NLS hierarchy. 1.4.4 AKNS system with u(N) reduction. 1.5 Darboux transformation and scattering, inverse scattering theory. 1.5.1 Outline of the scattering and inverse scattering theory for the 2 × 2 AKNS system . 1.5.2 Change of scattering data under Darboux transformations for su(2) AKNS system. 2. 2+1 Dimensional Integrable Systems.- 2.1 KP equation and its Darboux transformation. 2.2 2+1 dimensional AKNS system and DS equation. 2.3 Darboux transformation. 2.3.1 General Lax pair. 2.3.2 Darboux transformation of degree one. 2.3.3 Darboux transformation of higher degree and the theorem of permutability. 2.4 Darboux transformation and binary Darboux transformation for DS equation. 2.4.1 Darboux transformation for DSII equation. 2.4.2 Darboux transformation and binary Darboux transformation for DSI equation. 2.5 Application to 1+1 dimensional Gelfand-Dickey system. 2.6 Nonlinear constraints and Darboux transformation in 2+1 dimensions. 3. N + 1 Dimensional Integrable Systems.- 3.1 n + 1 dimensional AKNS system. 3.1.1 n + 1 dimensional AKNS system. 3.1.2Examples. 3.2 Darboux transformation and soliton solutions. 3.2.1 Darboux transformation. 3.2.2 u(N) case. 3.2.3 Soliton solutions. 3.3 A reduced system on Rn. 4. Surfaces of Constant Curvature, Bäcklund Congruences.- 4.1 Theory of surfaces in the Euclidean space R3. 4.2 Surfaces of constant negative Gauss curvature, sine-Gordon equation and Bäcklund transformations. 4.2.1 Relation between sine-Gordon equation and surface of constant negative Gauss curvature in R3. 4.2.2 Pseudo-spherical congruence. 4.2.3 Bäcklund transformation. 4.2.4 Darboux transformation. 4.2.5 Example. 4.3 Surface of constant Gauss curvature in the Minkowski space R2,1 and pseudo-spherical congruence. 4.3.1 Theory of surfaces in the Minkowski space R2,1. 4.3.2 Chebyshev coordinates for surfaces of constant Gauss curvature. 4.3.3 Pseudo-spherical congruence in R2,1. 4.3.4 Bäcklund transformation and Darboux transformation for surfaces of constant Gauss curvature in R2,1. 4.4 Orthogonal frame and Lax pair. 4.5 Surface of constant mean curvature. 4.5.1 Parallel surface in Euclidean space. 4.5.2 Construction of surfaces. 4.5.3 The case in Minkowski space. 5. Darboux Transformation and Harmonic Map.- 5.1 Definition of harmonic map and basic equations. 5.2 Harmonic maps from R2 or R1,1 to S2, H2 or S1,1. 5.3 Harmonic maps from R1,1 to U(N). 5.3.1 Riemannian metric on U(N). 5.3.2 Harmonic maps from R1,1 to U(N). 5.3.3 Single soliton solutions. 5.3.4 Multi-soliton solutions. 5.4 Harmonic maps from R2 to U(N). 5.4.1 Harmonic maps from R2 to U(N) and their Darboux transformations. 5.4.2 Soliton solutions. 5.4.3 Uniton. 5.4.4 Darboux transformation and singular Darboux transformation for unitons. 6. Generalized Self-Dual Yang-Mills and Yang-Mills-Higgs Equations.- 6.1 Generalized self-dual Yang-Mills flow. 6.1.1 Generalized self-dual Yang-Mills flow. 6.1.2 Darboux transformation. 6.1.3 Example. 6.1.4 Relation with AKNS system. 6.2 Yang-Mills-Higgs### Andere boeken die eventueel grote overeenkomsten met dit boek kunnen hebben:

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