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The tanh method. II: Perturbation technique for conservative systems. (English) Zbl 0942.35035

Summary: With the aid of the tanh method, nonlinear wave equations are solved in a perturbative way. First, the KdV-Burgers 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 MKdV-Burgers equation is investigated in the same limit and similar results are obtained.
For Part I, ibid. 563-568 (1996) see Zbl 0942.35034 above.

MSC:

35C05 Solutions to PDEs in closed form
35Q53 KdV equations (Korteweg-de Vries equations)

Citations:

Zbl 0942.35034
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