Jacobi forms and Kaneko--Zagier type equations

For modular forms, the Kaneko--Zagier equation is a second-order differential equation with respect to the Serre derivative. Analogously, for Jacobi forms, there exists an analogue of the Serre derivative that increases the weight of a Jacobi form by 2 and preserves its index. It is not difficult to describe the kernel of this operator, but finding solutions of even second-order differential equations, known as Kaneko--Zagier type equations, is not such a trivial problem. In my talk, I will present some current progress on this topic.