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KdV ’95 pp 5-37 | Cite as

Integrability, Computation and Applications

  • M. J. Ablowitz
  • S. Chakravarty
  • B. M. Herbst

Abstract

The study of integrable systems and the notion of integrability has been re-energized with the discovery that infinite-dimensional systems such as the Korteweg-de Vries equation are integrable. In this paper, the following novel aspects of integrability are described: (i) solutions of Darboux, Brioschi, Halphen-type systems and their relationships to monodromy problems and automorphic functions, (ii) computational chaos in integrable systems, (iii) we explain why we believe that homoclinic structures and homoclinic chaos associated with nonlinear integrable wave problems, will be observed in appropriate laboratory experiments.

Key words

integrability KdV equation nonlinear integrable wave functions monodromy problems automorphic functions 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • M. J. Ablowitz
    • 1
  • S. Chakravarty
    • 1
  • B. M. Herbst
    • 2
  1. 1.Program in Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of Applied MathematicsThe University of the Orange Free StateBloemfonteinSouth Africa

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