in this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for l^2(r^d). further, we illustrate our results with some examples and applications.

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...

In this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for L2(Rd). Further, we illustrate our results with some examples and applications.