Input—Output Systems and Bäcklund Transformations
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The concept of input-output system is stated in the geometric language of infinite jets. It is proved that finite-dimensional input-output mappings are Bäcklund transformations. This assertion is generalized to infinite-dimensional input-output systems. Observability conditions are derived as a consequence of the geometric interpretation introduced.
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This work was supported by the Russian Foundation for Basic Research, projects nos. 19-07-00817 and 18-07-00269.
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