  A nonlinear evolution equation for wave packet surface gravity waves with
variation in topography is revisited in this article. The equation is modeled
by a spatial inhomogeneous nonlinear Schr\"odinger (NLS) equation with varying
coefficients, derived by Djordjevi\'c and Redekopp (1978) and the nonlinear
coefficient is later corrected by Dingemans and Otta (2001). We show
analytically and qualitatively that the nonlinear coefficient and the
corresponding averaging value, stated but not derived, by Benilov, Flanagan and
Howlin (2005) and Benilov and Howlin (2006) are inaccurate. For a particular
choice of topography and wave characteristics, the NLS equation alternates
between focusing and defocusing case and hence, it does not admit the formation
of a classical soliton, neither bright nor dark one.
