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.
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Ablowitz, M.J., Chakravarty, S. & Herbst, B.M. Integrability, computation and applications. Acta Appl Math 39, 5–37 (1995). https://doi.org/10.1007/BF00994624
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DOI: https://doi.org/10.1007/BF00994624