With the aid of the tanh method, nonlinear wave equations are solved in a perturbative way. First, the KdVBurgers equation is investigated in the limit of weak dispersion. As a result, a general shock wave profile, with a perturbative solitary-wave contribution superposed, emerges. For a particular choice of the parameters, a comparison with the exact solution is made. Further, the MKdVBurgers is investigated in the same limit and similar results are obtained.
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Malfliet et al. (1996) studied this question.
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