Scaling Symmetry Reductions of Coupled KdV Systems
Abstract
In this paper we discuss the Painlevé reductions of coupled KdV systems. We start by comparing the procedure with that of {\em stationary reductions}. Indeed, we see that exactly the same construction can be used at each step and parallel results obtained. For simplicity, we restrict attention to the $t_2$ flow of the KdV and DWW hierarchies and derive respectively 2 and 3 compatible Poisson brackets, which have identical {\em structure} to those of their stationary counterparts. In the KdV case, we derive a discrete version, which is a non-autonomous generalisation of the well known Darboux transformation of the stationary case.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.09694
- arXiv:
- arXiv:2405.09694
- Bibcode:
- 2024arXiv240509694F
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- 35Q53;
- 37J37;
- 37K05;
- 70H06
- E-Print:
- 11 pages