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The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis.
Purobi Rani Kundu1, Md Rezwan Ahamed Fahim1, Md Ekramul Islam1
1Department of Mathematics, Pabna University of Science and Technology, Bangladesh.
Heliyon
|March 31, 2021
Summary
Researchers extended the sine-Gordon expansion method to solve higher-dimensional nonlinear evolution equations (NLEEs). This approach successfully found steady soliton solutions for the Estevez-Mansfield-Clarkson and Riemann wave equations, confirming its effectiveness.
Area of Science:
- Nonlinear science
- Mathematical physics
- Applied mathematics
Background:
- The Estevez-Mansfield-Clarkson (EMC) and Riemann wave (RW) equations are crucial in nonlinear science with applications in plasma physics, fluid dynamics, and optics.
- The standard sine-Gordon expansion (SGE) method is typically limited to lower-dimensional nonlinear evolution equations (NLEEs).
Purpose of the Study:
- To extend the sine-Gordon expansion (SGE) method for analyzing higher-dimensional nonlinear evolution equations (NLEEs).
- To establish steady soliton solutions for the Estevez-Mansfield-Clarkson (EMC) and Riemann wave (RW) equations using the developed method.
Main Methods:
- Development of an extended higher-dimensional sine-Gordon expansion method.
- Application of the extended SGE method to find soliton solutions for EMC and RW equations.
- Graphical analysis of solutions by varying parameters to understand solution characteristics.
Main Results:
- The extended SGE method was successfully developed and applied to higher-dimensional NLEEs.
- Numerous soliton solutions were obtained for the EMC and RW equations, validating the method's compatibility.
- Solution characteristics were found to be dependent on parameter choices, visualized through graphs.
Conclusions:
- The extended SGE method is effective for finding soliton solutions to higher-dimensional NLEEs.
- This approach offers a valuable tool for analyzing complex nonlinear phenomena.
- The study highlights the significant impact of parameter selection on the behavior of soliton solutions.
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