Matrix Integrals and Several Integrable Differential-Difference Systems

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  • Hu Xing-Biao
    Institute of Computational Mathematics and Scientific Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
  • Zhao Jun-Xiao
    Department of Mathematics, Graduate University of Chinese Academy of Sciences
  • Li Chun-Xia
    Department of Mathematical Sciences, Tsinghua University

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In this paper, the relations between three special forms of matrix integrals and their associated integrable differential-difference systems are considered. It turns out that these matrix integrals with special β=2 and 1,4 satisfy the differential-difference KP equation, the two-dimensional Toda lattice, the semi-discrete Toda equation and their Pfaffianized systems, respectively.

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