TABLE OF CONTENTS Motivated by the experiments and conclusions presented by Mr. Russell in the Report of the Fourteenth Meeting of the British Association for the Advancement of Science, Stokes (1847) developed the classical solution for nonlinear surface gravity waves in order to prove that the speed of nonlinear surface gravity waves (or the velocity of propagation) depends on the amplitude of the wave by applying the method of successive approximations that is now commonly referred to as Stokes perturbation (Dean and Dalrymple, 1991, Chapter 11.2). However, the perturbation technique was developed by Poincare and Van Zeipel (Nayfeh, 1981) more than 50 years after Stokes published his solution. The method of successive approximations will lead to results similar to perturbation, but it is more tedious to apply than perturbation and it has no method for suppressing resonant forcing (viz., perturbing either the frequency ?=2 ? f or the wave celerity C). Stokes applied a 2D coordinate system with the vertical y axis positive down from the still-water-level (SWL); and recovered the fluid velocity vector from a scalar velocity potential 
(x, y, t) by positive spatial derivatives according to
where the ordinary derivative notation d/dx was applied instead of the contemporary partial derivative notation ?/ ?x and ?/ ?y. Stokes proposed the following boundary value problem (BVP) for a scalar velocity potential (x, y, t) (Stokes, 1847, p. 200):
