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A note on Bernoulli polynomials and solitons
Abstract:Abstract

The dependence on time of the moments of the one-soliton KdV solutions is given by Bernoulli polynomials. Namely, we prove the formula /></span>expressing the moments of the one-soliton function sech<sup>2</sup>(<i>x-t</i>) in terms of the Bernoulli polynomials <i>Bn</i>(<i>x</i>). We also provide an alternative short proof to the Grosset-Veselov formula connecting the one-soliton to the Bernoulli numbers <span class= /></span>(D?=?d/dx) published recently in this journal.</td> </tr> <tr> <td align=
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