(untitled) (Journal of Applied Science and Engineering A, 2024)
We study the Cauchy problem of a system of dissipative nonlinear Schr¨odinger equations. Our target is to obtain a time-decay estimate of the solutions in L^2 without size-restriction on the initial data. By imposing high regularity and rapid spatial decay on the initial data, we find that the L^2-norm of the solutions decays at the rate of O((t)^−2/5) as t → ∞. It is a refined decay-estimate, compared to former works.