Analytic smoothing effect for system of nonlinear Schrödinger equations with general mass resonance

Abstract

We prove the analytic smoothing e¤ect for solutions to the system of nonlinear Schrödinger equations under the gauge invariant nonlinearities. This result extends the known result due to Hoshino [Nonlinear Differential Equations Appl. 24 (2017), Art. 62]. Under rapidly decaying condition on the initial data, the solution shows a smoothing effect and is real analytic with respect to the space variable. Our theorem covers not only the case for the gauge invariant setting but also multiple component case with higher power nonlinearity up to the fifth order.