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Springerplus. 2013 Jul 18;2:326. doi: 10.1186/2193-1801-2-326. eCollection 2013.

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

Author information

  • 1Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh ; School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.

Abstract

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

KEYWORDS:

Auxiliary equation; Extended tanh-function method; Further improved (G'/G)-expansion method; The breaking soliton equation; Traveling wave solutions

PMID:
23961400
[PubMed]
PMCID:
PMC3736072
Free PMC Article
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