Volume 7, Issue 1, February 2000, Pages 22 - 33
On the Calculation of Finite-Gap Solutions of the KdV Equation
Received 16 July 1999, Revised 11 September 1999, Accepted 16 September 1999, Available Online 1 February 2000.
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- 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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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 -