United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS MODULATIONAL INSTABILITY AND EXACT SOLUTIONS FOR THE DISCRETE COMPLEX CUBIC QUINTIC GINZBURG-LANDAU EQUATION OF AN OPEN BOSE-EINSTEIN CONDENSATION

In this paper, we investigate analytically and numerically the modulational instability in a model of nonlinear physical systems like nonlinear periodic lattices. This model is described by the discrete complex cubic quintic Ginzburg-Landau equation with non-local quintic term. We produce characteristics of the modulational instability in the form of typical dependences of the instability growth rate (gain) on the perturbation wavenumber and the system’s parameters. Excellent agreement has been obtained between analytical and numerical study. Further, we derive the periodic function and new type of solitary wave solutions for the above system. By using the extended Jacobian elliptic function approach, we obtain the exact stationary solitons and periodic wave solutions of this equation. These solutions include, Jacobian periodic wave solution, alternating phase Jacobi periodic wave solution, kink and bubble soliton solutions, alternating phase kink soliton alternating phase bubble soliton solutions.