Asymptotic expansions of the amplitudes of the direct and scattered waves in a waveguide system with an imperfection core are derived for large core number and the partial cancellation of the direct wave by the scattered wave is shown in detail. The total power of light in the cross section of a waveguide system is analytically derived and it is shown that the total power of the sum of the direct and scattered waves decreases from that of the direct wave because of the cancellation, the difference of the total power transfers to the localized wave and the total power of light is conserved.