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Updated: May 8, 2026

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
Published on: October 20, 2023
Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of
M Ali Akbar1, Norhashidah Hj Mohd Ali, Syed Tauseef Mohyud-Din
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.
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