| Abstract: | We consider the solution of the Korteweg–de Vries (KdV) equation  with periodic initial value  where C , A , k , μ, and β are constants. The solution is shown to be uniformly bounded for all small ɛ, and a formal expansion is constructed for the solution via the method of multiple scales. By using the energy method, we show that for any given number T > 0 , the difference between the true solution v ( x , t ; ɛ) and the N th partial sum of the asymptotic series is bounded by ɛ N +1 multiplied by a constant depending on T and N , for all −∞ < x < ∞, 0 ≤ t ≤ T /ɛ , and 0 ≤ɛ≤ɛ0 . |
