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PP. 1-5

Open Access

Auxiliary Function Method for Nonlinear Partial Differential Equations

Haiming Fu, Zhengde Dai

International Journal of Partial Differential Equations and Applications. 2013, 1(1), 1-5

Publication Date (Web): 12 September 2013

DOI: 10.12691/ijpdea-1-1-1

Abstract: A new auxiliary function method is given, and some exact solutions of the auxiliary function are given too. As an example, Reaction-diffusion equation and BBM-Burgers equation are solved. Obviously, the auxiliary function method can be applied to solve other type of nonlinear partial differential equations as well.

Figure 1 of 3

PP. 6-12

Open Access

Enhanced (G’/G)-Expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics

Md. Ekramul Islam, Kamruzzaman Khan, M. Ali Akbar, Rafiqul Islam

International Journal of Partial Differential Equations and Applications. 2013, 1(1), 6-12

Publication Date (Web): 12 November 2013

DOI: 10.12691/ijpdea-1-1-2

Abstract: In the present paper, we construct the traveling wave solutions involving parameters for the (2+1)-dimensional cubic Klein-Gordon equation (cKG) via Enhanced (G’/G)-expansion method. The efficiency of this method for finding these exact solutions has been demonstrated. As a result, a set of solitary wave solutions are derived, which are expressed by the combinations of rational, hyperbolic and trigonometric functions involving several parameters. It is shown that the method is effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics.