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Explicit solutions of the Bogoyavlensky-Konoplechenko equation. (English) Zbl 1184.35285
Summary: By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the Bogoyavlensky-Konoplechenko equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the BK equation. Then we get the reductions using the symmetry and give some exact solutions of the BK equation.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35C05 Solutions of PDE in closed form 35B06 Symmetries, invariants, etc. (PDE)
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##### References:
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