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Asymptotic Analysis of a Perturbed Periodic Solution for the KdV Equation

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We consider the solution of the Korteweg–de Vries (KdV) equation with periodic initial value where C, A, k, , and  are constants. The solution is shown to be uniformly bounded for all small , 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; ) and the Nth partial sum of the asymptotic series is bounded by N+1 multiplied by a constant depending on T and N, for all −∞ < x < ∞, 0 ≤tT/ , and 0 ≤≤0 .
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Document Type: Research Article

Affiliations: 1: Beijing University of Chemical Technology 2: City University of Hong Kong

Publication date: January 1, 2006

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