The method of geometrical optics, based on Hamilton's equations is applied to investigating light propagation in multimode fibers with refractive index profile having parabolic and fourth-order terms. Nonlinear dependence of profile dispersion on the refractive index has been taken into account. optimum distribution of the refractive index of germanium doped silica fiber with large NA which minimizes monochromatic rms pulse width and rms in the spectral range of LED source, has been determined.