Malfliet, Willy; Hereman, Willy The tanh method. I: Exact solutions of nonlinear evolution and wave equations. (English) Zbl 0942.35034 Phys. Scr. 54, No. 6, 563-568 (1996). Summary: A systemized version of the tanh method is used to solve particular evolution and wave equations. If one deals with conservative systems, one seeks travelling-wave solutions in the form of a finite series in tanh. If present, boundary conditions are implemented in this expansion. The associated velocity can then be determined a priori, provided the solution vanishes at infinity. Hence, exact closed-form solutions can be obtained easily in various cases. For Part II, ibid. 569-575 (1996) see Zbl 0942.35035 below. Cited in 2 ReviewsCited in 325 Documents MSC: 35C05 Solutions to PDEs in closed form 35Q53 KdV equations (Korteweg-de Vries equations) Citations:Zbl 0942.35035 Software:MACSYMA PDFBibTeX XMLCite \textit{W. Malfliet} and \textit{W. Hereman}, Phys. Scr. 54, No. 6, 563--568 (1996; Zbl 0942.35034) Full Text: DOI