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Nonlinear switching of ultrashort pulses in two-core, three-core, and four-core optical fibers is analyzed theoretically by solving a set of generalized, linearly coupled nonlinear Schrödinger equations. The analysis takes into account the effects of the coupling coefficient dispersion (or intermodal dispersion) in the fiber, which have been overlooked in previous studies of three-core and four-core fibers. It is shown that the coupling coefficient dispersion can break up ultrashort pulses over a short length of a multicore fiber and consequently deteriorate the switching characteristics. In general, the coupling coefficient dispersion leads to an increase in the switching power and a reduction in the switching contrast and the sharpness of the switching transition. The three-core fiber is more tolerant to the coupling coefficient dispersion and therefore the preferred choice for the implementation of an all-fiber nonlinear optical switch.