Group Analysis of Differential Equations and Integrable Systems − 2018
Charalambos Evripidou
(La Trobe University,
Bundoora, Victoria,
Australia)
Dressing the dressing chain
Abstract:
The dressing chain (DC) arises in the application of Darboux
transformations to the
Schödinger equation, which is the spectral problem for the Kortewegde
Vries (KdV)
equation. It also arises as an autoBäcklund transformation of the modified
KdV equation (mKdV) via the celebrated Miura transformation between KdV and
mKdV. Odd dimensional periodic reductions of the DC were shown to be
Liouville
integrable by Veselov and Shabat. In this talk I will demonstrate what
happens if
we replace the KdV by the DC in the above text:
The lattice KdV equation (lKdV) arises in the application of Darboux
transformations
to the discrete Schödinger equation, which is the spectral problem for
the DC. It
also arises as an autoBäcklund transformation of a modified DC (mDC)
via a Bäcklund
transformation between DC and mDC. Odd dimensional periodic reductions
of the
lKdV equation are shown to be Liouville integrable.
