论文标题
矢量修改的KDV层次结构的敷料
Dressing for a vector modified KdV hierarchy
论文作者
论文摘要
我们介绍了与修改后的Korteweg-De Vries方程的多组分概括相关的层次结构和孤子解决方案。提供了用于获得与层次结构较高流相关的LAX运算符的递归公式。使用理性敷料的方法和LAX算子的对称性，我们获得了一soliton溶液。我们还得出了一般等级的一只呼吸道解决方案，并用决定因素表达它。我们介绍了一只呼吸器溶液的最简单情况，该溶液是由两个恒定的单位向量彼此正常的参数化。最后，我们获得了层次结构相关的Bäcklund变换。
We present the hierarchy and soliton solutions associated to a multi-component generalisation of the modified Korteweg-de Vries equation. A recursive formula for obtaining the Lax operators associated to the higher flows of the hierarchy is provided. Using the method of rational dressing and the symmetries of the Lax operators we obtain the one-soliton solution. We also derive the general rank one-breather solution and express it in terms of determinants. We present the simplest case of the one-breather solution, which is parametrised by two constant unit vectors normal to each other. Finally, we obtain the associated Bäcklund transformation for the hierarchy.
