An integrable semi-discretization of the modified Camassa-Holm equation with linear dispersion term
数学公众报告(120周年校庆系列第15场)
报告题目(Title)：An integrable semi-discretization of the modified Camassa-Holm equation with linear dispersion term
报告人(Speaker)：虞国富 教授（上海交通大学数学科学学院）
地点(Place)：腾讯会议：453 850 0147
时间(Time)：4月8日(周五)，15:00-16:00
邀请人(Inviter)：王灯山
报告摘要
In this talk, we present an integrable discretization of a modified Camassa-Holm equation with linear dispersion term. The key of the construction is the semi-discrete analogue for a set of bilinear equations of the modified Camassa-Holm equation. Firstly, we show that these bilinear equations and their determinant solutions either in Gram-type or Casorati-type can be reduced from the discrete KP equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solution in Gram-type or Casorati-type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, we are able to derive an integrable semi-discrete analogue of the modified Camassa-Holm equation. It is also shown that the semi-discrete modified Camassa-Holm equation converges to the continuous one in the continuum limit. This is a joint work with Bao-Feng Feng and Han-Han Sheng.
主讲人简介
虞国富教授，2007年6月博士毕业于中国科学院数学与系统科学研究院; 加拿大蒙特利尔大学博士后。现为上海交通大学数学科学学院教授、博士生导师，数学科学学院副院长。主要从事孤立子与可积系统、特殊函数、正交多项式方面的研究。在数学物理领域学术刊物上发表SCI论文40余篇。主持国家自然科学基金、上海市晨光计划、上海交通大学晨星青年学者奖励计划等多项研究课题。
