The nonlinear equation governing the non-propagating solitary wave and its analytical solution in a channel with uniformly and slowly varying width has been derived using the perturbation theory of multiple scales. The result obtained predicts that the solitary wave always moves towards the narrow end of the channel with an approximately uniform acceleration which is proportional to the variation rate of the width. The method in the present paper can be extended in principle to the theoretical investigation of other linear and nonlinear waves in a uniformly and slowly varying wave guide.