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A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations
Md Shafiqul Islam1, Kamruzzaman Khan1, M Ali Akbar2
1Department of Mathematics , Pabna University of Science and Technology , Pabna 6600, Bangladesh.
Royal Society Open Science
|June 12, 2015
Summary
This study introduces an improved F-expansion method with the Riccati equation to find exact solutions for nonlinear evolution equations. The technique effectively identifies all solution branches, proving useful for complex wave phenomena in physics and engineering.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
- Engineering Mathematics
Background:
- Nonlinear evolution equations are fundamental in describing complex phenomena across science and engineering.
- Finding exact solutions for these equations is crucial for theoretical understanding and practical applications.
- Existing numerical techniques can struggle with distinguishing closely related multiple solutions.
Purpose of the Study:
- To introduce a novel analytical method for obtaining exact solutions to nonlinear evolution equations.
- To demonstrate the method's capability in simultaneously calculating all solution branches.
- To verify the method's efficiency and applicability using established nonlinear wave equations.
Main Methods:
- The improved F-expansion method combined with the Riccati equation.
- Analytical formulation of exact travelling wave solutions.
- Application to the modified Benjamin-Bona-Mahony (mBBM) equation and the modified Korteweg-de Vries (mKdV) equation.
Main Results:
- The proposed method successfully generates exact travelling wave solutions.
- It efficiently calculates all solution branches, even when they are numerically indistinguishable.
- Demonstrated effectiveness on the mBBM and mKdV equations.
Conclusions:
- The improved F-expansion method with the Riccati equation is a powerful and straightforward analytical tool.
- This method offers a reliable approach for solving nonlinear wave equations in mathematical physics and engineering.
- It provides a significant advancement for researchers seeking exact solutions in nonlinear dynamics.
Keywords:
NLEEsexact solutionimproved -expansion methodmodified Benjamin–Bona–Mahony equationmodified Korteweg-de Vries equationMore Related Videos
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