Abstract: In this paper, the solitary waves in an arbitrary cross-section channel which gradually changes in the streamwise have been studied. The KdV equation with slowly varying coefficients is derived. Thus, we produced the first term of its asymptotic solution, travel speed of solitary waves and the relation between the amplitude of wave and the geometric size of channel. The results have been applied to the cases of triangular and rectangular channels. For the channel with varying depths and breadths they are fairly consistent with those of Johnson, Shuto and Mile.

Key words: the non-local theory, Schmidt’s method, the triple-integral equation