Self-similarity and asymptotic stability for coupled nonlinear Schrِdinger equations in high dimensions

This paper is concerned with systems of coupled Schrödinger equations with polynomial nonlinearities and dimension n ≥ 1 . We show the existence of global self-similar solutions and prove that they are asymptotically stable in a framework based on weak- L p spaces, whose elements have local finite L 2 -mass. The radial symmetry of the solutions is also addressed.