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The algebraic structures underlying integrability

P M Santini

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The author presents a unified approach to describe the algebraic properties of integrable systems, identifying an abstract and elementary operator structure underlying integrability and showing that well known and novel examples of integrable equations are generated by different concrete realisations of this structure. In addition, the author shows that the calculation of trivial commutators can be used to select the concrete realisations which give rise to integrable systems.


PACS

02.10.De Algebraic structures and number theory

02.30.Tb Operator theory

02.30.Ik Integrable systems

MSC

08Axx Algebraic structures (See also 03C05)

Subjects

Mathematical physics

Dates

Issue 1 (February 1990)


A Corrigendum for this article has been published in 1990 Inverse Problems 6 479


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