E. M. E. ZAYED,Adbul-Ghani AL-NOWEHY.The Riccati Equation Method Combined with the Generalized Extended \$(G'/G)\$-Expansion Method for Solving the Nonlinear KPP Equation[J].数学研究及应用,2017,37(5):577~590
The Riccati Equation Method Combined with the Generalized Extended \$(G'/G)\$-Expansion Method for Solving the Nonlinear KPP Equation
The Riccati Equation Method Combined with the Generalized Extended \$(G'/G)\$-Expansion Method for Solving the Nonlinear KPP Equation

DOI：10.3770/j.issn:2095-2651.2017.05.008

 作者 单位 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

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.

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.