“…To the best of our knowledge, the so-called "method of moment for nonlinear Schrödinger equation" [20], with its possibilities to reduce the problem to a system of coupled ordinary nonlinear differential equations is one of the best candidate for this approach. Furthermore, the method provides approximations which receive different names depending on the specific field of application: time-dependent variational method, collective coordinates method, the averaged Lagrangian [21,22] and the so-called quadratic phase approximation [20]. The results shown for the evolution of the field solution using the moments method are exact and in some sense rigorous.…”