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Wednesday, May 13, 2020 | History

7 edition of Darboux transformations in integrable systems found in the catalog.

Darboux transformations in integrable systems

theory and their applications to geometry

by Chaohao Gu

  • 270 Want to read
  • 11 Currently reading

Published by Springer in Dordrecht .
Written in English

    Subjects:
  • Darboux transformations,
  • Integral geometry

  • Edition Notes

    Includes bibliographical references (p. [301]-308) and index.

    Statementby Chaohao Gu, Hesheng Hu and Zixiang Zhou.
    SeriesMathematical physics studies -- v. 26.
    ContributionsHu, Hesheng, 1928-, Zhou, Zixiang.
    Classifications
    LC ClassificationsQC174.26.W28 G8 2005, QC174.26.W28 G8 2005
    The Physical Object
    Paginationx, 308 p. :
    Number of Pages308
    ID Numbers
    Open LibraryOL18228149M
    ISBN 101402030878, 1402030886

    Darboux integrals are equivalent to Riemann integrals, meaning that a function is Darboux-integrable if and only if it is Riemann-integrable, and the values of the two integrals, if they exist, are equal. The definition of the Darboux integral has the advantage of being easier to apply in computations or proofs than that of the Riemann integral.   The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric.

    Get this from a library! Darboux transformations in integrable systems: theory and their applications to geometry. [Chaohao Gu; Hesheng Hu; Zixiang Zhou] -- 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. Share - Mathematical Physics Studies: Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry 26 by Hesheng Hu, Zixiang Zhou and Chaohao Gu (, Paperback) Mathematical Physics Studies: Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry 26 by Hesheng Hu, Zixiang Zhou and Chaohao Gu .

    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 Author: Chaohao Gu, Hesheng Hu and Zixiang Zhou. Kou, Xin, "Rogue Wave Solutions to Integrable System by Darboux Transformation" ().Graduate College Dissertations and Theses. techniques for finding solutions of integrable equations [25]. Darboux transformation the one given in Matveev’s book [25] Author: Xin Kou.


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Darboux transformations in integrable systems by Chaohao Gu Download PDF EPUB FB2

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 by: 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 cturer: Springer.

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.

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 book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the.

Preface.- 1. 1+1 Dimensional Integrable Systems.- KdV equation, MKdV equation and their Darboux transformations. Original Darboux transformation. Darboux transformation for KdV equation. Darboux transformation for MKdV equation. Examples: single and double soliton solutions. Relation between Darboux transformations.

Online version of book available online through link above; subscription required to access content. Recommended Citation. Anderson, I.

and Fels, M. Transformations of Darboux Integrable Systems in Differential equations: Geometry, symmetries and integrability: the Abel Symposiumproceedings of the Fifth Abel Symposium, Tromsø Cited by: 6.

Darboux integrable equations are certain ODE systems known as equations of Lie type and this led, for the first time, to a group theoretical formulation of the method I.M.

Anderson. viii DARBOUX TRANSFORMATIONS IN INTEGRABLE SYSTEMS Generalized self-dual Yang-Mills flow Darboux transformation Example Relation with AKNS system Yang-Mills-Higgs field in 2+1 dimensional MinkowskiFile Size: 1MB.

Pris: kr. Häftad, Skickas inom vardagar. Köp Darboux Transformations in Integrable Systems av Chaohao Gu, Anning Hu, Zixiang Zhou på Several types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered.

We also present solutions such as supersolitons and superkinks. Abstract. This article reviews some recent theoretical results about the structure of Darboux integrable differential systems and their relationship with symmetry reduction of exterior differential systems.

The symmetry reduction representation of Darboux integrable equations is then used to derive some new and unusual by: 6. 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.

On the other hand, the Lax–Darboux scheme constitutes an important tool in the theory of integrable systems, as it relates several concepts of integrability. 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.

N discrete integrable system, Darboux transformations, tau function, discrete Gel’ fand–Dikii hierarchy 1. Introduction Discrete integrable systems have played an increasingly prominent part in mathematical phys-ics.

A number of intriguing connections have emerged between the field of discrete integrable. Darboux transformations in theory of integrable systems Sergey V. Smirnov Moscow State University Research Seminar Nazarbaev University, Astana Sergey V.

Smirnov Darboux transformations in theory of integrable systems. 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.

Darboux transformations constitute a very important tool in the theory of integrable systems. They map trivial solutions of integrable partial differential equations to non-trivial ones and they link the former to discrete integrable systems.

On the other hand, they can be used to construct Yang-Baxter maps which can be restricted to completely. In this context, a Darboux transformation is another form of the Lie-B¨acklund-Darboux transformation. Like the B¨acklund transformations, the derivation method for Darboux transformations is often of “experimental” nature.

The popular ones include the “dressing method” [84] and the Chen’s method [25]. Binary Darboux Transformation for the Modified Kadomtsev Petviashvili Equation Hu Xiao-Rui and Chen Yong-Recent citations Soliton elastic interactions and dynamical analysis of a reduced integrable nonlinear Schrödinger system on a triangular-lattice ribbon Hao-Tian Wang and Xiao-Yong Wen-Darboux transformations and exactCited by: 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.

Abstract: This volume represents the Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia.

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.Presents the Darboux transformations in matrix form and provides algebraic algorithms for constructing the explicit solutions.

This work elucidates the behavior of simple and multi-solutions, even in Read more.