Abstract
We introduce an elementary operator structure and we show that well-known examples of integrable systems like the Korteweg-de Vries, the Nonlinear Schrodinger, the Benjamin-Ono, the Chiral fields, the Kadomtsev-Petviashvili, the Davey-Stewartson and the self-dual Yang Mills equations are generated by different concrete realizations of it. We also show that the simplest realization of this structure gives rise to nonlinear algebraic equations which share with their differential analogues the basic features of integrability and therefore are examples of solvable nonlinear algebraic systems.
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© 1989 Springer-Verlag
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Santini, P.M. (1989). Solvable nonlinear equations as concrete realizations of the same abstract algebra. In: Balabane, M., Lochak, P., Sulem, C. (eds) Integrable Systems and Applications. Lecture Notes in Physics, vol 342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035677
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DOI: https://doi.org/10.1007/BFb0035677
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