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On the Exp-function method for constructing travelling wave solutions of nonlinear equations. (English) Zbl 1216.35109
Ma, Wen-Xiu (ed.) et al., Nonlinear and modern mathematical physics. Proceedings of the 1st international workshop held in Beijing, China, July 15–21, 2009. Melville, NY: American Institute of Physics (ISBN 978-0-7354-0755-8/pbk). AIP Conference Proceedings 1212, 280-285 (2010).
Summary: The Exp-function method or some similar direct methods have been applied by many researchers to the construction of “new” solutions to nonlinear differential equations. In this paper, we demonstrate that some of those so-called “new” solutions can always be transformed into a uniform formula, which can be obtained by a very simple integral in fact. Consequently, we have reasons to believe that it should take more careful checking of computations if “different” solutions generated by using the Exp-function method and some similar direct methods are really different from the known ones.
For the entire collection see [Zbl 1205.00092].

35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35A24 Methods of ordinary differential equations applied to PDEs