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http://dx.doi.org/10.14317/jami.2011.29.1_2.351

THE ($\frac{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)
Publication Information
Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 351-367 More about this Journal
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) -expansion method combined with the Riccati equation, where G = $G({\xi})$ satisfies the Riccati equation $G and A, B are arbitrary constants.
Keywords
The ($\frac{G)- expansion method; The Riccati equation; Traveling wave solutions; The KdV-mKdV equation; The KdVB equation; The cKG equation; The GZK-BBM equation; The mKdV-ZK equation;
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