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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,...
A brief historical review and recent developments of theories and experiments of optical solitons in fibers are presented with particular emphasis on their integrability and controllability in real systems.
We review the different aspects of integrable discretizations in space and time of the Korteweg-de Vries equation, including Miura transformations to related integrable difference equations, connections to integrable mappings, similarity reductions and discrete versions of Painlevé equations as...
In this paper I give a brief personal review of the history of the early soliton days and how they led to thevisiometrics and reduced modeling paradigm that has been a part of my approach to nonlinear science in the last three decades. I illustrate it with HEC (Hybrid Eiliptic-Contour): a fast,...
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