论文标题
Kundu-Eckhaus方程的向量形式及其最简单的解决方案
The vector form of Kundu-Eckhaus equation and its simplest solutions
论文作者
论文摘要
在我们的工作中，根据功能参数$ r $的不同，可集成向量非线性微分方程的层次结构是使用单构矩阵构建的。 $ r =α（\ Mathbf {p}^t \ Mathbf {q}）$的第一个等式是Kundu-Eckhaus方程的向量类似物。当$α= 0 $时，该层次结构的方程将变成Manakov系统层次结构的方程。提出了针对Kundu-Eckhaus和Manakov系统向量类似物的新椭圆解决方案。总而言之，可以表明，对于向量集成的非线性方程的解决方案存在线性转换为相同方程的其他解决方案。
In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations.
