A model and analysis for the nonlinear amplification of waves in the cochlea

A nonlinear three-dimensional model for the amplification of a wave in the cochlea is analyzed. Using the long-slender geometry of the cochlea, and the relatively high frequencies in the hearing spectrum, an asymptotic approximation of the solution is derived for linear, but spatially inhomogeneous, amplification. From this, a nonlinear WKB approximation is constructed for the nonlinear problem, and this is used to derive an efficient numerical method for solving the amplification problem. The advantage of this approach is that the very short waves needed to resolve the wave do not need to calculated as they are represented in the asymptotic solution.