Exponential decay of the solutions to nonlinear Schrödinger systems

Abstract: We show that the components of finite energy solutions to general nonlinear Schr\"odinger systems have exponential decay at infinity. Our results apply to positive or sign-changing components, and to cooperative, competitive, or mixed-interaction systems. As an application, we use the exponential decay to derive an upper bound for the least possible energy of a solution with a prescribed number of positive and nonradial sign-changing components.