The cochlea is known to be a nonlinear system that shows strong fluid-structure coupling. In this work, the monolithic state space approach to cochlear modeling [Rapson et al., J. Acoust. Soc. Am. 131, 3925-3952 (2012)] is used to study the inherent nature of this coupling. Mathematical derivations requiring minimal, widely accepted assumptions about cochlear anatomy provide a clear description of the coupling. In particular, the coupling forces between neighboring cochlear partition segments are demonstrated, with implications for theories of cochlear operation that discount the traveling wave hypothesis. The derivations also reaffirm the importance of selecting a physiologically accurate value for the partition mass in any simulation. Numerical results show that considering the fluid properties in isolation can give a misleading impression of the fluid-structure coupling. Linearization of a nonlinear partition model allows the relationship between the linear and nonlinear fluid-structure interaction to be described. Furthermore, the effect of different classes of nonlinearities on the numerical complexity of a cochlear model is assessed. Cochlear models that assume outer hair cells are able to detect pressure will require implicit solver strategies, should the pressure sensitivity be demonstrated. Classical cochlear models in general do not require implicit solver strategies.