We examine the excitation of breather structures in a degenerate relativistic plasma consisting of non-extensive electrons and cold ions. For this purpose, the multiple time scale perturbation technique is used to obtain a nonlinear Schrödinger equation (NLSE). We then consider different localized solutions regarding analytical breather solutions of the NLSE, and examine their properties in the frame of the present plasma system, i.e. a degenerate relativistic non-extensive plasma. The results of the present investigation may be useful for the understanding of the basic features of the nonlinear excitations that may occur in dense astrophysical plasmas.
