Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy
Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy
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DOI：
10.1016/j.nuclphysb.2020.114933
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发表时间：
2019-10
影响因子：
2.8
通讯作者：
P. Adamopoulou;G. Papamikos
中科院分区：
文献类型：
--
作者：
P. Adamopoulou;G. Papamikos
我们构造了一个多分量广义修正KdV方程的层次结构，并找到其相关成员的精确解。层次结构及其守恒律的构造是基于Drinfel 'd-Sokolov方案，然而，在我们的情况下，Lax算子包含底层李代数的常数非正则元素。我们还推导出相关的递归算子的层次使用的对称结构的拉克斯运营商。最后，利用有理修整方法得到了单孤子解，并得到了一般秩的单呼吸子解。
We construct the hierarchy of a multi-component generalisation of modified KdV equation and find exact solutions to its associated members. The construction of the hierarchy and its conservation laws is based on the Drinfel'd-Sokolov scheme, however, in our case the Lax operator contains a constant non-regular element of the underlying Lie algebra. We also derive the associated recursion operator of the hierarchy using the symmetry structure of the Lax operators. Finally, using the rational dressing method we obtain the one-soliton solution and we find the one-breather solution of general rank in terms of determinants.