Journal of Nonlinear Mathematical Physics

Volume 7, Issue 1, February 2000, Pages 22 - 33

On the Calculation of Finite-Gap Solutions of the KdV Equation

Authors
A.M. Korostil
Corresponding Author
A.M. Korostil
Received 16 July 1999, Revised 11 September 1999, Accepted 16 September 1999, Available Online 1 February 2000.
DOI
https://doi.org/10.2991/jnmp.2000.7.1.3How to use a DOI?
Abstract
A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass function. The calculation of initial elliptic finite-gap solutions is reduced to the solution of the finite-band equations with respect to the parameters of the representation. The time evolution of these solutions is described via the dynamic equations of their poles, integrated with the help of the finite-gap equations. The proposed approach is applied by calculating the elliptic 1-, 2- and 3-gap solutions of the KdV equations.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
7 - 1
Pages
22 - 33
Publication Date
2000/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2000.7.1.3How 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  - A.M. Korostil
PY  - 2000
DA  - 2000/02
TI  - On the Calculation of Finite-Gap Solutions of the KdV Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 22
EP  - 33
VL  - 7
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2000.7.1.3
DO  - https://doi.org/10.2991/jnmp.2000.7.1.3
ID  - Korostil2000
ER  -