论文标题
高阶KDV方程的椭圆解决方案
Elliptic Solutions for Higher Order KdV Equations
论文作者
论文摘要
我们从GL（2，$ \ Mathbb {r} $）$ \ cong $ SO（2,1）Lie Group的观点研究高阶KDV方程。我们发现高阶KDV方程的椭圆解直到第九阶。我们认为，三角/双曲/椭圆/椭圆形$ n $ -soliton解决方案的主要结构与原始KDV方程相同。指出差异仅是时间依赖性，我们发现可以通过正确替换时间依赖性来从原始KDV方程的高阶方程中的$ n $ - soliton解决方案构建。我们讨论所有高阶KDV方程始终存在椭圆解。
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.
