Malfliet, Willy; Hereman, Willy The tanh method. II: Perturbation technique for conservative systems. (English) Zbl 0942.35035 Phys. Scr. 54, No. 6, 569-575 (1996). 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. Cited in 1 ReviewCited in 169 Documents MSC: 35C05 Solutions to PDEs in closed form 35Q53 KdV equations (Korteweg-de Vries equations) Citations:Zbl 0942.35034 PDFBibTeX XMLCite \textit{W. Malfliet} and \textit{W. Hereman}, Phys. Scr. 54, No. 6, 569--575 (1996; Zbl 0942.35035) Full Text: DOI