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学术报告二十:虞国富—Miwa transformation and an integrable semi-discretization of the modified Camassa-Holm equation with linear dispersion term

时间:2022-04-20 作者: 点击数:

报告时间:2022年04月26日(星期15:00-16:00

报告地点:腾讯会议:845601604

人:虞国富 教授

工作单位:上海交通大学

举办单位:万象城官方网站(中国)有限公司

报告简介:

In this talk, we construct 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.


报告人简介:

虞国富,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。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。在国外重要学术刊物上发表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。


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