An Integrable Matrix Camassa-Holm Equation
An Integrable Matrix Camassa-Holm Equation
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可积矩阵 Camassa-Holm 方程
DOI：
10.1088/0253-6102/71/12/1399
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发表时间：
2019
影响因子：
3.1
通讯作者：
Ruguang Zhou
中科院分区：
文献类型：
--
作者：
Li-feng Chan;Bao-Qiang Xia;Ruguang Zhou
给出了一个可积sl（2）-矩阵Camassa-Holm（CH）方程.可积性意味着方程具有零曲率表示和无穷多个守恒律。该方程包含两个待定函数，它们满足一组约束条件，并可化为许多已知的多分量峰方程。我们找到了一种构造约束条件的方法，从而得到了许多新的矩阵CH方程。对于平凡约化矩阵CH方程，我们构造了它的N-峰子解。
We present an integrable sl(2)-matrix Camassa-Holm (CH) equation. The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws. This equation includes two undetermined functions, which satisfy a system of constraint conditions and may be reduced to a lot of known multicomponent peakon equations. We find a method to construct constraint condition and thus obtain many novel matrix CH equations. For the trivial reduction matrix CH equation we construct its N-peakon solutions.