FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 7, PAGES 101-116

**On skew-symmetric and general deformations of Lax pseudodifferential
operators**

B. A. Kupershmidt

Abstract

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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 $\{\; \backslash binom\{2n+1\}\{2s+1\}\; (4s+1-1)/(s+1)\; B$_{2s+2} }, 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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k067/k06707h.htm

Last modified: February 13, 2007