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By applying the theory and method of singular perturbations, we investigate the travelling wave solution of the KdVB equation under the assumption v2?4μ. We get the explicit expression of the travelling wave solution up to the third order atfirst. Then, we obtain the general asymptotic expansion: u=u(0)+εu(1)+ε1u(2)+…+εnu(n)+… and prove that u(j)(j=1,2,…,n,…) are bounded functions.
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