3 edition of **Bäcklund and Darboux transformations** found in the catalog.

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Published
**2001**
by American Mathematical Society in Providence, RI
.

Written in English

- Solitons -- Congresses.,
- Bäcklund transformations -- Congresses.,
- Darboux transformations -- Congresses.,
- Geometry, Differential -- Congresses.

**Edition Notes**

Includes bibliographical references.

Other titles | Geometry of solitons |

Statement | Alan Coley ... [et al.], editor. |

Genre | Congresses. |

Series | CRM proceedings & lecture notes -- v. 29 |

Contributions | Coley, A. A. |

Classifications | |
---|---|

LC Classifications | QC174.26.W28 A2 1999 |

The Physical Object | |

Pagination | xx, 436 p. : |

Number of Pages | 436 |

ID Numbers | |

Open Library | OL22465534M |

ISBN 10 | 0821828037 |

We explain the role of Darboux and Bäcklund transformations in the theory of integrable systems, and we show how they can be used to construct discrete integrable systems via the Lax–Darboux scheme. Moreover, we give an introduction to the theory of Yang–Baxter maps and we show its relation to discrete integrable ://~bilman/publication/discrete-integrable-book. grable Hamiltonian system. B¨acklund transformation originated from a quest for Lie’s second type invariant transformation rather than his tangent transformation. That brings the title of this book: Lie-B¨acklund-Darboux Transformations which refer to both B¨acklund transformations and Darboux

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We construct a local action of the group of rational maps from S 2 to GL(n,C) on local solutions of flows of the ZS-AKNS sl(n,C)-hierarchy. We show that the actions of simple elements (linear fractional transformations) give local Bäcklund transformations, and we derive a permutability formula from different ?doi= The N = 2 a = - 2 supersymmetric KdV equation is studied. A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation. The Bäcklund transformation and the related nonlinear superposition formula are used to construct integrable super semi-discrete

While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special These lecture notes are devoted to the integrability of discrete systems and their relation to the theory of Yang-Baxter (YB) maps. Lax pairs play a significant role in the integrability of discrete systems. We introduce the notion of Lax pair by considering the well-celebrated doubly-infinite Toda lattice. In particular, we present solution of the Cauchy initial value problem via the method

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This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory.

The book consists of two parts. The first is a series This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Bäcklund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory.

The book consists of two parts. The first is a series of introductory pedagogical lectures Buy Backlund and Darboux Transformations: The Geometry of Solitons (Crm Proceedings and Lecture Notes) on FREE SHIPPING on qualified.

Feb 6, A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation. Also, a nonlinear :// Get this from a library.

Bäcklund and Darboux transformations: geometry and modern applications in soliton theory. [C Rogers; W K Schief] -- This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory.

The authors also explore the extensive body of literature C. Gu and Z. Zhou, On the Darboux matrices of Bäcklund transformations for the AKNS system, Lett.

Math. Phys. 13 (), – MathSciNet Bäcklund and Darboux transformations book CrossRef Google Scholar 4. Conclusions and discussions. In conclusion, Darboux–Bäcklund transformation of A–L equation is constructed form the pseudopotential, from which breather and rogue wave solutions are derived and the corresponding dynamical properties are shown graphically.

Of course, there are still many problems that deserve further discussion, such as if there are other transformations that make :// Feb 6, A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation.

Also, a nonlinear superposition. Download Citation on ResearchGate | Bäcklund and Darboux Transformations | This book describes the remarkable connections that :// Amazon配送商品ならBaecklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory (Cambridge Texts in Applied Mathematics)が通常配送無料。更にAmazonならポイント還元本が多数。Rogers, C., Schief, W.

K.作品ほか、お急ぎ便 Find many great new & used options and get the best deals for Cambridge Texts in Applied Mathematics Ser.: Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory by W. Schief and C. Rogers (, Perfect) at the best online prices at › eBay › Books › Textbooks, Education & Reference › Adult Learning & University.

The theory of Darboux and Bäcklund transformations has been an integrated part of the soliton theory, and it is important for a given nonlinear system to find its Bäcklund transformations. With a Bäcklund transformation in hand, one may either construct various solutions for the associated nonlinear system or produce new integrable Book Review: Bäcklund and Darboux Transformations.

Geometry and Modern Applications in Soliton Theory. by C. Rogers and W.K. Schief Möbius, P. Abstract. Publication: Zeitschrift Angewandte Mathematik und Mechanik. Pub Date: May DOI: /zamm M/abstract. B¨acklund and Darboux Transformations This book describes the remarkable connections that exist between the classi-cal differential geometry of surfaces and modern soliton theory.

The authors explore the extensive body of literature from the nineteenth and early twen-tieth centuries by such eminent geometers as Bianchi, Darboux, B¨acklund, The topics dealt with cover a wide range of phenomena: solitons, integrable systems, Hamiltonian structures, Bäcklund and Darboux transformation, symmetries, fi- nite-dimensional dynamical systems, quantum and statistical mechanics, knot theory and braid group, R-matrix method, Hirota and Painlevé analysis, and applications to water waves The GBDT version of the Bäcklund–Darboux transformation is applied to the case of the harmonic maps and a new and simple algebraic procedure to construct new harmonic maps from the initial ones is given, using some methods from system theory.

A new general formula on the GBDT transformations of the Sym–Tafel immersions is Noté /5. Retrouvez Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory et des millions de livres en stock sur Achetez neuf ou d'occasion A Darboux Transformation for the Coupled Kadomtsev–Petviashvili Equation Yang Guang-You and Liu Qing-Ping Chinese Physics Letters 25 1 IOPscience.

Commutativity of Pfaffianization and Bäcklund transformations: the KP equation Xing-Biao Hu and Jun-Xiao Zhao Inverse Problems 21 Rogers / Schief, Bäcklund and Darboux Transformations,Buch, Bücher schnell und portofrei Bäcklund-Transformationen (im Englischen auch Baecklund oder Backlund geschrieben) sind Transformationen der abhängigen und unabhängigen Variablen in nichtlinearen Differentialgleichungen, die es ermöglichen, Lösungen einer Gleichung oder Lösungen verschiedener Gleichungen miteinander zu sind in der Theorie der Solitonen :// ISBN: OCLC Number: Description: xx, pages: illustrations ; 26 cm.

Contents: Backlund Transformations of the Higher Order Painleve Equations / V.I. Gromak --Dressing Method and Backlund and Darboux Transformations / D. Levi and O. Ragnisco --The Classical Geometry of Backlund uction to Applications in Soliton Theory / C. Rogers, C. and Schief, W.

Bäcklund and Darboux transformations: geometry and modern applications in soliton theory / C. Rogers, "This book describes the connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors explore the body of literature from the nineteenth and early.

(). Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications. Journal of Nonlinear Mathematical Physics: Vol.

25, No. 3, pp. In this book, the authors develop Darboux's idea to solve linear and nonlinear partial differential equations arising in soliton theory: the non-stationary linear Schrodinger equation, Korteweg-de Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS.

Panagiota Adamopoulou. a, Anastasia Doikou. a, ∗, Georgios Papamikos. b. a. Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.

b. Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United