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.

Biography

陈晓敏，2016年博士毕业于中国科学院数学与系统科学研究院，2016-2018年在德国马克斯普朗克动力学与自组织研究所做博士后。现为北京工业大学理学部讲师，硕士生导师。主要从事可积系统与正交多项式方面的交叉研究，学术成果发表在国际知名期刊 Adv. Math., Nonlinearity, Numerical Algorithms, Physica D，Studies in Applied Mathematics 等上面，主持国家自然科学青年基金项目、北京市自然科学青年基金项目以及北京市教委科技一般项目各一项。