Solving the constrained modified KP hierarchy by gauge transformations
Solving the constrained modified KP hierarchy by gauge transformations
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DOI：
10.1080/14029251.2019.1544787
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发表时间：
2018-12
影响因子：
0.7
通讯作者：
Huizhan Chen;Lumin Geng;Na Li;Jipeng Cheng
中科院分区：
文献类型：
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作者：
Huizhan Chen;Lumin Geng;Na Li;Jipeng Cheng
在本文中，我们主要研究 Kupershmidt-Kiso 版本中约束修正 KP 层次结构的两种规范变换。需要相应的规范变换来不仅保留 Lax 方程，而且保留 Lax 算子。为此，通过选择特殊的生成本征函数和伴随本征函数，修正的KP层次TD(Φ)=(Φ−1)−x1∂Φ−1和TI(Ψ)=Ψ−1∂−1Ψx的初等规范变换算子成为约束情况下的算子。最后，讨论了TD和TI在本征函数Φ和伴随本征函数Ψ上相应的连续应用。
In this paper, we mainly investigate two kinds of gauge transformations for the constrained modified KP hierarchy in Kupershmidt-Kiso version. The corresponding gauge transformations are required to keep not only the Lax equation but also the Lax operator. For this, by selecting the special generating eigenfunction and adjoint eigenfunction, the elementary gauge transformation operators of modified KP hierarchy TD(Φ) = (Φ−1)−x1∂ Φ−1 and TI (Ψ) = Ψ−1∂ −1Ψx, become the ones in the constrained case. Finally, the corresponding successive applications of TD and TI on the eigenfunction Φ and the adjoint eigenfunction Ψ are discussed.