The Static Elliptic $N$-soliton Solutions of the KdV Equation
Mathematical Physics
2019-06-24 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
Regarding -soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative B\"{a}cklund transformation, we have succeeded in constructing the KdV static elliptic -soliton solution, which means that we have constructed infinitely many solutions for the -function type differential equation.
Cite
@article{arxiv.1812.09685,
title = {The Static Elliptic $N$-soliton Solutions of the KdV Equation},
author = {Masahito Hayashi and Kazuyasu Shigemoto and Takuya Tsukioka},
journal= {arXiv preprint arXiv:1812.09685},
year = {2019}
}
Comments
10 pages, 3 figures