### Formal diagonalisation of the Lax-Darboux scheme and conservation laws of integrable partial
differential, differential-difference and partial difference

Mikhailov, A *(University of Leeds)*

Thursday 11 July 2013, 14:00-14:30

Seminar Room 1, Newton Institute

#### Abstract

Formal diagonalisation of Lax operators leads to formal diagonalisation of the corresponding Darboux transformations and vice versa. The latter enables us to find recurrent relations for generating conservation laws and establish natural relations between the canonical series of local conservation laws for partial differential, differential-difference and partial difference equations.
In particular we show that the canonical densities of conservation laws for the symmetries of partial difference equations are also conserved densities for the partial difference equations themselves.

#### Presentation

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