“…Equations of this type have many different applications in Physics, such as nonrelativistic limit of the Klein-Gordon equation [25,26,28], Langmuir wave envelope approximation in plasma physics [4], model of planar light bullets [2,34] and so forth. For this reason, it has been subject of investigation, both from a theoretical (see, e.g., [21]) and, more recently, also from a numerical point of view (see, e.g., [1,19,20,23,24,[29][30][31][32][33]). We here consider the case where the equation (1.1) is completed with the initial conditions: Consequently, both u 0 and v 0 will be assumed to be periodic functions, regular enough (as a periodic function).…”