Abstract
A de Sole, V G Kac and M Wakimoto have recently introduced a new family of compatible Hamiltonian operators of the form H(N,0) = D2 ∘ ((1/u) ∘ D)2n ∘ D, where N = 2n + 3, n = 0, 1, 2, …, u is the dependent variable and D 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 H(N,0). We also give the Darboux coordinates for H(N,0) for any odd N ⩾ 3.
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