Nambu-Poisson structures and their foliations.
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
Noncommutative root space Witt, Ricci flow, and Poisson bracket continual Lie algebras.
Nonlinear Schrödinger equation on four-dimensional compact manifolds
We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness for small energy...