Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE ($\frac{G'}{G}$)- EXPANSION METHOD COMBINED WITH THE RICCATI EQUATION FOR FINDING EXACT SOLUTIONS OF NONLINEAR PDES

  • Zayed, E.M.E. (Mathematics Department, Faculty of Science, Zagazig University)
  • Received : 2010.01.24
  • Accepted : 2010.08.31
  • Published : 2011.01.30
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Abstract

In this article, we construct exact traveling wave solutions for nonlinear PDEs in mathematical physics via the (1+1)- dimensional combined Korteweg- de Vries and modified Korteweg- de Vries (KdV-mKdV) equation, the (1+1)- dimensional compouned Korteweg- de Vries Burgers (KdVB) equation, the (2+1)- dimensional cubic Klien- Gordon (cKG) equation, the Generalized Zakharov- Kuznetsov- Bonjanmin- Bona Mahony (GZK-BBM) equation and the modified Korteweg- de Vries - Zakharov- Kuznetsov (mKdV-ZK) equation, by using the (($\frac{G'}{G}$) -expansion method combined with the Riccati equation, where G = $G({\xi})$ satisfies the Riccati equation $G'({\xi})=A+BG^2$ and A, B are arbitrary constants.

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