Geodesic
On skew-symmetric and general deformations of Lax pseudodifferential operators
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 7, pp. 101-116

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A nonlinear deformation is conjectured for the reduction of the third KP flow on the subspace of skew-symmetric operators, and the conjecture is proved for the linearized flow. As a by-product, we find a peculiar (nonquantum) polynomial deformation of the numbers $\left\{\binom{2n+1}{2s+1}\frac{4^{s+1}-1}{s+1}B_{2s+2}\right\}$, where $B_m$'s are the Bernoulli numbers. General open questions and generalizations are also discussed. The conjecture is extended to all the flows, and its linearized version is proved. 
@article{FPM_2006_12_7_a7,
     author = {B. A. Kupershmidt},
     title = {On skew-symmetric and general deformations of {Lax} pseudodifferential operators},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {101--116},
     publisher = {mathdoc},
     volume = {12},
     number = {7},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_7_a7/}
}
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B. A. Kupershmidt. On skew-symmetric and general deformations of Lax pseudodifferential operators. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 7, pp. 101-116. http://geodesic.mathdoc.fr/item/FPM_2006_12_7_a7/