LAUSR

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 ut+iuxx+i|u|2u+γu=f,f∈𝕃2(ℝ). “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)?”