English

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 NN-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 NN-soliton solution, which means that we have constructed infinitely many solutions for the \wp-function type differential equation.

Keywords

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