3 research outputs found
The Darboux coordinates for a new family of Hamiltonian operators and linearization of associated evolution equations
A. de Sole, V. G. Kac, and M. Wakimoto (arXiv:1004.5387) have recently
introduced a new family of compatible Hamiltonian operators of the form
, where , ,
is the dependent variable and is the total derivative with respect to
the independent variable. We present a differential substitution that reduces
any linear combination of these operators to an operator with constant
coefficients and linearizes any evolution equation which is bi-Hamiltonian with
respect to a pair of any nontrivial linear combinations of the operators
. We also give the Darboux coordinates for for any odd
.Comment: 6 pages, AMS-LaTeX, extended versio