On some properties of a discrete hungry Lotka-Volterra system of multiplicative type

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Two kinds of discrete hungry Lotka-Volterra systems (dhLV) are known as discretizations of the additive type hungry Lotka-Volterra system and the multiplicative one. By associating the dhLV of additive type (dhLVI) and the discrete hungry Toda equation (dhToda) with LR transformations, some of the authors give a Bäcklund transformation between these two systems. In this paper, from the dhLV of multiplicative type (dhLVII), we first derive the qd-type dhLVII. Through finding the positivity of the qd-type dhLVII and the LR transformation associated with the dhLVII, we present Bäcklund transformations among the dhLVI, the dhLVII and the dhToda. Moreover, by using one of the Bäcklund transformations, we show asymptotic convergence of the qd-type dhLVII.
Faculty of Mathematics, Kyushu University,九州大学大学院数理学研究院の論文