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Taking as starting point the planar model arising from the dimensionalreduction of the Abelian-Higgs Carroll-Field-Jackiw model, we write down andstudy the extended Maxwell equations and the corresponding wave equations forthe potentials. The solutions for these equations correspond to the usual onesfor the MCS-Proca system, supplemented with background-dependent correctionterms. In the case of a purely timelike background, exact algebraic solutionsare presented which possess a similar behavior to the MCS-Proca counterpartsnear and far from the origin. On the other hand, for a purely spacelikebackground, only approximate solutions are feasible. They consist ofnon-trivial analytic expressions with a manifest evidence of spatialanisotropy, which is consistent with the existence of a privileged direction inspace. These solutions also behave similarly to the MCS-Proca ones near and farfrom the origin.Comment: 15 pages, 5 figures, style Revtex 4, revised version To appear in  Eur. Phys. J. C (2005

Classical solutions in a Lorentz violating scenario of Maxwell-Chern-Simons-Proca electrodynamics