报告题目:Bogoyavlensky-mKdV hierarchy and toroidal Lie algebra

报告人：程纪鹏 教授（中国矿业大学）

报告时间：2023.08.24 19:30-20:30

报告地点：腾讯会议 811275449

报告摘要：By principal representation of toroidal Lie algebra sl_2^{tor}, we construct an integrable system: Bogoyavlensky-mKdV (B-mKdV) hierarchy, which is (2+1)-dimensional generalization of mKdV hierarchy. Firstly, bilinear equation of B-mKdV hierarchy is obtained by fermionic representation of  sl_2^{tor} and boson-fermion correspondence. Then other equivalent formulations of B-mKdV are discussed, including wave function, dressing operator and Lax equation.  After that, Miura links between Bogoyavlensky-KdV hierarchy and B-mKdV hierarchy are discussed. Finally, we construct soliton solutions of B-mKdV hierarchy.

报告人简介：程纪鹏，中国矿业大学数学学院教授、博士生导师，江苏高校＂青蓝工程＂优秀青年骨干教师。研究方向：数学物理与可积系统。目前在Adv Math,  Int Math Res Not，Sci China Math，J Math Phys等期刊发表科研论文近60篇。主持在研国家自然科学基金面上项目一项。

邀请人：马立媛