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Zbl 1136.35451
Yomba, Emmanuel
The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations. (English)
[J] Phys. Lett., A 336, No. 6, 463-476 (2005). ISSN 0375-9601

Summary: An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs.

MSC 2000:: *35Q53 KdV-like equations
35Q35 Other equations arising in fluid mechanics

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Zentralblatt MATH Berlin [Germany]