Veranstaltungen

In this talk, we consider 2-coupled systems of nonlinear Schrödinger equations with cubic nonlinearities. One typical system in this class is the Manakov model. In the first part, we consider the classification of 2-coupled systems. The complete list of standard forms of systems with Hamiltonian structure is given. This is due to a representation of a system in terms of a pair of a matrix and a vector which clarifies the Hamiltonian structure of the systems. In the second part, we consider standing-wave solutions to the standard forms. To this end, we introduce an abstract treatment that is applicable to a wider class of N-coupled systems. It turns out that the existence / nonexistence and the shape of the ground state are well-described by the function determining the nonlinear potential part.

Virasoro constraints are conjectural differential equations satisfied by generating functions of descendant Gromov-Witten invariants of Kahler manifolds/orbifolds. In this talk, we will begin with reviewing Givental's formulation of these constraints. We will then discuss the following result, which is a joint work with T. Coates and A. Givental: For a toric bundle E-> B, Virasoro constraints hold for E if and only if they hold for B.