Quasideterminant solutions of a non-Abelian Hirota–Miwa equation
Quasideterminant solutions of a non-Abelian Hirota–Miwa equation
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DOI：
10.1088/1751-8113/40/42/s07
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
C. Gilson;J. Nimmo;Y. Ohta
中科院分区：
文献类型：
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作者：
C. Gilson;J. Nimmo;Y. Ohta
考虑了Hirota-Miwa方程的一个非阿贝尔版本。在Nimmo(2006 J.Phys.)的早期论文中。答：数学。Gen.395053-65)，它展示了如何通过达布变换为该系统构造以拟行列式表示的解。本文从不同的角度讨论了这些解，证明了这些解是准Plücker坐标的，并且非阿贝尔Hirota-Miwa方程可以写成准Plücker关系。文中还考虑了矩阵Hirota-Miwa方程的特例，采用了一种更传统的双线性方法，并对各种方法进行了比较。
A non-Abelian version of the Hirota–Miwa equation is considered. In an earlier paper of Nimmo (2006 J. Phys. A: Math. Gen. 39 5053–65) it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper, we discuss these solutions from a different perspective and show that the solutions are quasi-Plücker coordinates and that the non-Abelian Hirota–Miwa equation may be written as a quasi-Plücker relation. The special case of the matrix Hirota–Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared.