in this case, the system supports similar soliton solutions, showing that the small distance behav- ior of the potential does not affect the presence of localized solutions. This is clearly seen in Figs. (7) and (8) where we show the corresponding solutions | ψ$_{1}$ | 2 and | ψ$_{2}$ | $^{2}$, for the periodic and quasiperiodic choices of χ ( t ) considered above. Due to the presence of a dark-like solution, which does not vanish in the limit x → ±∞ , the numerical method used in the former two examples fails to work in such a case. This, therefore, requires seeking alternative numerical algorithm to circumvent this problem. We are currently investigating this issue. In summary, in this paper we have presented soliton solutions for two coupled nonlinear Schr¨odinger equations modulated in the space and time. This model is robust in the sense of presenting a vast quantity of nontrivial solutions in the systems with modulations in space and time of the traps and nonlinearities. We have considered three different examples of potentials and nonlinearities. All these solutions are of great interest in several areas, such that, in coupled Bose- Einstein condensates and communications in optical fibers.Our work can potentially motivate future studies and help guide possible experimental work in superchemistry and fluid dynamics in general. This work was supported by the CAPES, CNPq, FAPESP, FUNAPE-GO and the Instituto Na- cional de Ciˆencia e Tecnologia da Informac¸˜ao Quˆantica- MCT. I. ACKNOWLEDGMENTS [1] Y. Kivshar, G.P. Agrawal, Optical solitons: form fibers t o photonic crystals, Academic, New York, 2003. [2] B.A. Malomed, Soliton manegement in periodic systems, Springer, New York, 2006. [3] T. Ueda, W.L. Kath, Phys. Rev. A 42 (1990) 563; [4] L.P. Pitaevskii, S. Stringari, Bose-Einstein Condensation, Oxford U. P., Oxford, 2003. [5] C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge U. P., Cambridge 2002. [6] E. Timmermans, P. Tommasini, M. Hussein, A. Kerman, Physics Report 315 (1999) 199. 8 J. Yang, Phys. Rev. E 59 (1999) 2393.