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The presentation of explicit analytical solutions of a class of nonlinear evolution equations. (English) Zbl 1198.35221

Summary: We introduce a function set \(\Omega^m\). There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in \(\Omega^m\). A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
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