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“…One method for analytically constructing a nonlinear wave solution to a reaction-diffusion equation is to exploit conditional integrability and construct a solution through dominant balance provided the equation passes the Painlevé test. This approach was used in the construction of an exact solution to Fisher's equation in (Ablowitz and Zeppetella, 1979), and has been applied to study a variety of other conditionally integrable reaction or reaction-diffusion equations; for more information, see (Goriely, 1996;Hearns et al, 2012;Ramani et al, 1989;Russo et al, 2013;Weiss et al, 1983;Weiss, 1983). To begin, consider the case of = 0, so that we have (13).…”

confidence: 99%

“…One method for analytically constructing a nonlinear wave solution to a reaction-diffusion equation is to exploit conditional integrability and construct a solution through dominant balance provided the equation passes the Painlevé test. This approach was used in the construction of an exact solution to Fisher's equation in (Ablowitz and Zeppetella, 1979), and has been applied to study a variety of other conditionally integrable reaction or reaction-diffusion equations; for more information, see (Goriely, 1996;Hearns et al, 2012;Ramani et al, 1989;Russo et al, 2013;Weiss et al, 1983;Weiss, 1983). To begin, consider the case of = 0, so that we have (13).…”

confidence: 99%

“…Seeking exact solutions of these equations plays an important role in the study of these nonlinear physical phenomena. In the past several decades, many effective methods for obtaining exact solutions of these equations have been presented, such as the inverse scattering method (Ablowitz and Clarkson, 1991), Hirota bilinear method (Hirota, 1980), Backlund transformation (Hirota, 1980;Miura, 1978), Painleve expansion (Hearns et al, 2012;Kudryashov, 1988;Kudryashov, 1990;Kudryashov, 1991;Russo et al, 2012;Weiss et al, 1983), Sine-Cosine method (Wazwaz, 2004;, Jacobi elliptic function method (Lu, 2005;Liu et al, 2001), Tanh-function method (Fan, 2000;Yusufoglu and Bekir, 2008;Zayed and Abdel Rahman, 2010;Zhang and Xia, 2008), F-expansion method (Zhang and Xia, 2006), Exp-function method (Bekir, 2010; 2009; He and Wu, 2006), (G'/G)-expansion method (Bekir, 2008;Islan, 2010;Kudryashov, 2010;Kudryashov, 2009;Ma et al, 2011;Peng, 2008Peng, , 2009Reza and Rasoul, 2011;Wang et al, 2008;Zayed, 2009;Zayed and Al-Joudi, 2010;Zayed and Al-Joudi, 2009;Zhang et al, 2011), the modified (G'/G)-expansion method (Ma et al, 2011;Reza and Rasoul, 2011;Wang et al, 2008) and so on. …”

confidence: 99%