A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”