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The tanh method. I: Exact solutions of nonlinear evolution and wave equations. (English) Zbl 0942.35034

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.


MSC:
35C05Solutions of PDE in closed form
35Q53KdV-like (Korteweg-de Vries) equations
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