On the semi-discrete Toda and sine-Gordon systems
数学专题报告
报告题目(Title)：On the semi-discrete Toda and sine-Gordon systems
报告人(Speaker)：李春霞 教授 （首都师范大学）
地点(Place)：后主楼1223
时间(Time)：4月20日(周日)，10:00-11:00
邀请人(Inviter)：臧立名、王灯山
报告摘要
Cauchy matrix approach is applied to generate the semi-discrete Toda equation, the modified semi-discrete Toda equation and their discrete Miura transformation in a systematic way. Furthermore, Lax pair is derived for the modified semi-discrete Toda equation. Solutions for the semi-discrete Toda equation are classified according to the canonical forms of the constant matrices in the corresponding Sylvester equation. The semi-discrete sine-Gordon equation, the modified semi-discrete sine-Gordon equation and their Miura transformation are constructed both by Cauchy matrix approach and by the 2-periodic reductions of the semi-discrete Toda system. Lax pair and diverse solutions including kink solutions and breathers are presented for the semi-discrete sine-Gordon equation. The connections of tau functions for both of the semi-discrete Toda equation and the semi-discrete sine-Gordon equation with Cauchy matrix approach are established.
主讲人简介
李春霞，首都师范大学数学科学学院教授，博士生导师，研究方向为孤子理论与可积系统。中国科学院博士，清华大学博士后，格拉斯哥大学博士后（英国皇家学会资助）。访问剑桥大学牛顿数学科学研究所、美国University of South Florida和College of Charleston。曾主持国家自然科学基金项目3项、北京市自然科学基金面上项目2项等。曾在Journal of Nonlinear Science, Proceedings of the Royal Society A, Journal of Physics A和Inverse Problems等刊物上发表论文。
