A Super Camassa–Holm Equation with N‐Peakon Solutions
A Super Camassa–Holm Equation with N‐Peakon Solutions
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DOI：
10.1111/j.1467-9590.2012.00555.x
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发表时间：
2013-01
影响因子：
2.7
通讯作者：
X. Geng;Bo Xue;Lihua Wu
中科院分区：
文献类型：
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作者：
X. Geng;Bo Xue;Lihua Wu
提出了一个具有峰子解的超级Camassa-Holm方程，它与一个具有两个位势的3 × 3矩阵谱问题相关联.借助于零曲率方程，我们导出了一族超Harry Dym型方程，并建立了它们的Hamilton结构.证明了超Camassa-Holm方程在族中是一个负流，且存在N个峰的精确解.作为例子，给出了超Camassa-Holm方程的精确单峰解.分别得到了超Camassa-Holm方程和超Harry Dym型方程的大量守恒量。
A super Camassa–Holm equation with peakon solutions is proposed, which is associated with a 3 × 3 matrix spectral problem with two potentials. With the aid of the zero‐curvature equation, we derive a hierarchy of super Harry Dym type equations and establish their Hamiltonian structures. It is shown that the super Camassa–Holm equation is exactly a negative flow in the hierarchy and admits exact solutions with N peakons. As an example, exact 1‐peakon solutions of the super Camassa–Holm equation are given. Infinitely many conserved quantities of the super Camassa–Holm equation and the super Harry Dym type equation are, respectively, obtained.