Non-commutative lattice-modified Gel'fand-Dikii systems

作者：Doliwa Adam^*

来源：Journal of Physics A-Mathematical and Theoretical, 2013, 46(20): 205202.

DOI：10.1088/1751-8113/46/20/205202

We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogues of themodified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and show directly the multidimensional consistency of these Gel'fand-Dikii-type equations. We demonstrate how the systems can be obtained as periodic reductions of the non-commutative lattice Kadomtsev-Petviashvilii hierarchy. The geometric description of the hierarchy in terms of Desargues maps helps to derive a non-isospectral generalization of the non-commutative lattice-modified Gel'fand-Dikii systems. We show also how arbitrary functions of single arguments appear naturally in our approach when making commutative reductions, which we illustrate on the non-isospectral non-autonomous versions of the lattice-modified Korteweg-de Vries and Boussinesq systems.

• 出版日期2013-5-24