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

This paper is concerned with systems of coupled Schrödinger equations with polynomial nonlinearities and dimension n≥1n≥1. We show the existence of global self-similar solutions and prove that they are asymptotically stable in a framework based on weak-LpLp spaces, whose elements have local finite L2L2-mass. The radial symmetry of the solutions is also addressed.

► We study systems of coupled Schrödinger equations with polynomial nonlinearities.
► We show the existence of global self-similar solutions.
► These solutions are asymptotically stable in a framework based on weak-LpLp spaces.
► Our results cover domain dimensions n≥1n≥1.
► The radial symmetry of the solutions is analyzed.