Journal of Nonlinear Mathematical Physics

Volume 14, Issue 2, April 2007, Pages 174 - 178

A note on Bernoulli polynomials and solitons

Authors
Khristo N BOYADZHIEV
Corresponding Author
Khristo N BOYADZHIEV
Available Online 2 April 2007.
DOI
https://doi.org/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.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
14 - 2
Pages
174 - 178
Publication Date
2007/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2007.14.2.3How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Khristo N BOYADZHIEV
PY  - 2007
DA  - 2007/04
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  - https://doi.org/10.2991/jnmp.2007.14.2.3
ID  - BOYADZHIEV2007
ER  -