Refined L^2-decay estimate of solutions to a system of dissipative nonlinear Schroedinger equations (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 $O((\log t)^{−2/5})$ as $t → ∞$. It is a refined decay-estimate, compared to former works.