A note on Bernoulli polynomials and solitons

DOI

10.2991/jnmp.2007.14.2.3How to use a DOI?

Abstract

The dependence on time of the moments of the one-soliton KdV solutions is given by Bernoulli polynomials. Namely, we prove the formula R x n sech 2 (x − t) dx = 2 π n (−i) n Bn ( 1 2 + t π i) , expressing the moments of the one-soliton function sech 2 (x−t) in terms of the Bernoulli polynomials Bn (x). We also provide an alternative short proof to the Grosset-Veselov formula connecting the one-soliton to the Bernoulli numbers R D m−1 sech 2 x 2 dx = (−1) m−1 2 2m+1 B2m , (D = d/dx) published recently in this journal.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Khristo N. Boyadzhiev
PY  - 2007
DA  - 2007/04/01
TI  - A note on Bernoulli polynomials and solitons
JO  - Journal of Nonlinear Mathematical Physics
SP  - 174
EP  - 178
VL  - 14
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.2.3
DO  - 10.2991/jnmp.2007.14.2.3
ID  - Boyadzhiev2007
ER  -