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arXiv · 2003.00005

Elliptic Solutions for Higher Order KdV Equations

Masahito Hayashi·Kazuyasu Shigemoto·Takuya Tsukioka
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Abstract

We study higher order KdV equations from the GL(2,$\mathbb{R}$) $\cong$ SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the trigonometric/hyperbolic/elliptic $N$-soliton solutions for higher order KdV equations is the same as that of the original KdV equation. Pointing out that the difference is only the time dependence, we find $N$-soliton solutions of higher order KdV equations can be constructed from those of the original KdV equation by properly replacing the time-dependence. We discuss that there always exist elliptic solutions for all higher order KdV equations.

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Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka. 2020-02-28. Elliptic Solutions for Higher Order KdV Equations. https://doi.org/10.1088/2399-6528%2Fab88df

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