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Soliton solutions for the nonlinear Zoomeron equation applying the modified Khater method
Aqsa Saleem1, Muhammad Abbas2, Magda Abd El-Rahman3
1Department of Mathematics, University of Sargodha, 40100, Sargodha, Pakistan.
Scientific Reports
|June 2, 2026
Summary
Researchers used the modified Khater method (MKM) to find new analytical solutions for the nonlinear Zoomeron equation, crucial for modeling wave propagation in physics. This method successfully uncovered diverse wave solutions, advancing understanding of nonlinear dynamics.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Wave Propagation
Background:
- The nonlinear Zoomeron equation is vital for modeling wave phenomena in fluid dynamics and nonlinear optics.
- Finding analytical solutions for this highly nonlinear equation presents significant challenges.
Purpose of the Study:
- To explore and derive exact analytical solutions for the nonlinear Zoomeron equation.
- To demonstrate the efficacy of the modified Khater method (MKM) for solving complex nonlinear evolution equations.
Main Methods:
- The modified Khater method (MKM) was employed to transform the nonlinear partial differential equation into an ordinary differential equation.
- Exact solutions were constructed using the MKM framework.
Main Results:
- A wide array of new analytical solutions were discovered, including kink, anti-kink, singular periodic, and dark solitary wave solutions.
- The dynamical behavior of these solutions was visualized using 2D, 3D, and contour plots in Mathematica.
- The MKM proved to be an effective tool for analyzing nonlinear evolution equations.
Conclusions:
- The derived solutions expand the known solution set for the Zoomeron model.
- The findings offer deeper insights into complex nonlinear wave dynamics, beneficial for future research in theoretical and applied physics.
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