Integrability conditions for difference equations
Seminar Room 1, Newton Institute
AbstractThe existence of an infinite hierarchy of symmetries is used as a definition for the integrability of difference equations. Using this definition and introducing the notion of a formal recursion operator, we derive some easily verifiable conditions which are necessary for the integrability of a given difference equation. We refer to these relations as integrability conditions and we show how symmetries and conservation laws can be derived from them. Employing these conditions, we establish the integrability of a particular equation and construct its symmetries. Finally, we derive a Miura transformation which maps these symmetries to a generalized Bogoyavlensky lattice.
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