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The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the
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.
Springerplus
|September 7, 2013
Summary
A modified (G/G)-expansion method generates new exact traveling wave solutions for nonlinear wave equations. This advanced technique offers an efficient tool for solving complex mathematical physics problems.
Area of Science:
- Mathematical Physics
- Nonlinear Partial Differential Equations
- Wave Equations
Background:
- The (G'/G)-expansion method is a common technique for finding traveling wave solutions.
- Existing methods may have limitations in generating diverse exact solutions.
Purpose of the Study:
- To present a modified alternative (G'/G)-expansion method.
- To construct new exact traveling wave solutions by incorporating the generalized Riccati equation.
- To demonstrate the method's efficacy on the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation.
Main Methods:
- Modification of the alternative (G'/G)-expansion method.
- Introduction of the generalized Riccati equation.
- Application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation.
Main Results:
- Abundant new exact traveling wave solutions were obtained for the DSW equation.
- The modified method provides a uniform approach to finding these solutions.
- The obtained solutions hold significance for explaining physical phenomena.
Conclusions:
- The modified alternative (G'/G)-expansion method is an efficient and advanced tool.
- This approach is effective for solving nonlinear partial differential equations in mathematical physics.
- The method facilitates the discovery of novel exact solutions.
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