rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Darboux Transformations in Integrable Systems
    sub title: Theory and their Applications to Geometry
  name:
    name part: Gu, Chaohao.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Hu, Hesheng.
    role:
      role term: author.
  name:
    name part: Zhou, Zixiang.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2005
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 308 p. online resource.
  abstract: 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.
  table of contents: 1+1 Dimensional Integrable Systems -- 2+1 Dimensional Integrable Systems -- N + 1 Dimensional Integrable Systems -- Surfaces of Constant Curvature, Bäcklund Congruences and Darboux Transformation -- Darboux Transformation and Harmonic Map -- Generalized Self-Dual Yang-Mills Equations and Yang-Mills-Higgs Equations -- Two Dimensional Toda Equations and Laplace Sequences of Surfaces in Projective Space.
  note: by Chaohao Gu, Hesheng Hu, Zixiang Zhou.
  subject:
    topic: Physics
  subject:
    topic: Differential geometry
  subject:
    topic: Physics
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Differential Geometry
  classification: QC19.2-20.85
  classification: 530.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Mathematical Physics Studies ; 26
  identifier: 9781402030888
  identifier: http://dx.doi.org/10.1007/1-4020-3088-6
  record info:
    record creation date: 100301
    record change date: 20151030111426.0
    record identifier: 978-1-4020-3088-8