Abstract

In this talk, I will introduce some works on extensions of certain integrable systems, including nonisospectral extensions of the semi-discrete Volterra lattices and Schur flow, a generalized discrete Lotka-Volterra equation, a generalized epsilon algorithm and an extension of the hungry Lotka-Volterra lattice to nonzero boundaries. We also present their corresponding molecule solutions expressed explicitly by determinant. Moreover, we investigate the relations between these integrable systems and orthogonal polynomials. All these results are obtained by Hirota’s bilinear method and determinant techniques.