题目:The extended q-deformed KdV hierarchy and a certain generalized Frobenius manifold

摘要: We consider a certain extension of the q-deformed KdV hierarchy, and show that it coincides with the topological deformation of the Principal Hierarchy associated with a special one dimensional generalized Frobenius manifold with non-flat unity.

报告人：张友金教授，清华大学

时间：2024年3月2日（周六）13:30-14:30

题目: On Integrability of several two-component bi-Hamiltonian systems

摘要: Recently, by combining the tri-duality of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators, Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonian operators.Then, those trios were used to construct bi-Hamiltonian systems which, as they claimed, includes some known systems and some apparently new ones. In this talk, we consider those apparently new systems and construct their Lax representations. Furthermore, we explore the possible connections between these systems and the existing ones.

报告人：刘青平教授，中国矿业大学（北京）

时间：2024年3月2日（周六）14:30-15:30

题目：半离散KP和mKP及其平方本征函数对称

摘要：我们引入Lax三重组，利用拟差分算子来构造标量的微分-差分KP方程族，并介绍此方程族的Hamilton结构与对称。该方程族的平方本征函数对称引出的约束可以建立上述Lax三重组及其伴随形式（称为“微分-差分KP系统”）与半离散的AKNS谱问题和半离散AKNS方程族之间的联系。该谱问题可以视为连续的AKNS谱问题的一种双向离散和Darboux变换。对于微分-差分modified KP (mKP)系统，平方本征函数对称约束引出相对论Toda系统以及半离散的导数Schrödinger (Chen-Lee-Liu (CLL))系统，得到的半离散CLL谱问题即为连续的CLL谱问题的Darboux变换。除了相对论Toda系统以外，上述结果与连续的KP和mKP的相关结果通过统一的连续极限相对应。此外，相对论Toda和半离散CLL都可以约化到半离散Burgers，后者可以视为Burgers方程族的Bäcklund变换，其非线性叠加公式即为离散的Burgers方程，具有3D相容性并且可以线性化。

报告人：张大军教授，上海大学

时间：2024年3月2日（周六）16:00-17:00

报告地点：第五教学楼5207教室