The Riccati Equation Method Combined with the Generalized Extended $(G'/G)$-Expansion Method for Solving the Nonlinear KPP Equation
Received:October 28, 2016  Revised:November 23, 2016
Key Word: the generalized extended $(G'/G)$-expansion method   the Riccati equation method   the nonlinear KPP equation   exact solutions   solitary wave solutions   periodic wave solutions  
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Author NameAffiliation
E. M. E. ZAYED Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt 
Adbul-Ghani AL-NOWEHY Department of Mathematics, Faculty of Education and Science, Taiz University, Taiz, Yemen 
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      An analytic study of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation is presented in this paper. The Riccati equation method combined with the generalized extended $(G'/G)$-expansion method is an interesting approach to find more general exact solutions of the nonlinear evolution equations in mathematical physics. We obtain the traveling wave solutions involving parameters, which are expressed by the hyperbolic and trigonometric function solutions. When the parameters are taken as special values, the solitary and periodic wave solutions are given. Comparison of our new results in this paper with the well-known results are given.
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