We consider the Nonlinear Schrödinger equation with a general nonlinearity (like a sum of powers), and we look for solitons that minimize locally the energy at fixed mass, without minimizing it globally. As such, variational approaches do not work, and we provide a method to construct such objects. We also show that it is possible to have arbitrarily many of them for well chosen nonlinearities.
This is a joint work with Simona Rota Nodari (Université Côte d'Azur)