The supersymmetric Camassa–Holm equation and geodesic flow on the superconformal group
The supersymmetric Camassa–Holm equation and geodesic flow on the superconformal group
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DOI：
10.1063/1.1330196
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发表时间：
1998-11
影响因子：
1.3
通讯作者：
C. Devchand;J. Schiff
中科院分区：
文献类型：
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作者：
C. Devchand;J. Schiff
我们研究了Camassa-Holm方程的一类费米子扩展。在这个家族中，我们确定了三种有趣的类型：(a)方程，它们是固有的哈密顿方程，描述二维超共形变换群上H1度规的测地流，(b)方程是关于不同哈密顿结构的哈密顿方程，以及(c)超对称方程。类(a)和(b)没有交集，但类(a)和(c)的交集给出了一个具有有趣的可积性的系统。我们证明了该系统的一些简单但不平凡的约简的Painleve性质，并讨论了峰值型解。
We study a family of fermionic extensions of the Camassa–Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently Hamiltonian, describing geodesic flow with respect to an H1 metric on the group of superconformal transformations in two dimensions, (b) equations which are Hamiltonian with respect to a different Hamiltonian structure and (c) supersymmetric equations. Classes (a) and (b) have no intersection, but the intersection of classes (a) and (c) gives a system with interesting integrability properties. We demonstrate the Painleve property for some simple but nontrivial reductions of this system, and also discuss peakon-type solutions.