Modified reductive perturbation method Waves in water of variable depth Korteweg-de Vries hierarchy a b s t r a c tIn this work, we extended the application of ''the modified reductive perturbation method'' to long waves in water of variable depth and obtained a set of KdV equations as the governing equations. Seeking a localized travelling wave solution to these evolution equations we determine the scale function c 1 (τ ) so as to remove the possible secularities that might occur. We showed that for waves in water of variable depth, the phase function is not linear anymore in the variables x and t. It is further shown that, due to the variable depth of the water, the speed of the propagation is also variable in the x coordinate.