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Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization
Bacui Li1, Fuzhang Wang2, Sohail Nadeem3
1Scientific Research Department, Party School of CPC Fushun, Fushun, Liaoning, China.
Plos One
|May 21, 2024
Summary
Researchers found new exact solutions for the Hirota equation using advanced mathematical methods. These novel bright and dark solitary wave solutions may help model complex nonlinear physical phenomena.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
Background:
- Nonlinear partial differential equations (PDEs) are crucial for modeling complex phenomena in physics and engineering.
- The Hirota equation is a significant integrable nonlinear PDE with diverse applications.
Purpose of the Study:
- To derive explicit and exact solutions for the Hirota equation.
- To explore novel solitary wave solutions, including bright, dark, and bell profiles.
- To demonstrate the applicability of the employed methods to other nonlinear PDEs.
Main Methods:
- Application of the power-exponential function method.
- Utilization of the extended hyperbolic auxiliary equation method.
- Employing a subsidiary elliptic-like equation and a simple transformation.
Main Results:
- Explicit solutions for the subsidiary elliptic-like equation were obtained.
- Exact solutions for the Hirota equation were successfully derived.
- New bright solitary wave, dark solitary wave, bell profile solitary wave, and Jacobian elliptic function solutions were identified.
Conclusions:
- The developed methods provide a powerful approach for solving nonlinear PDEs.
- The newly found solutions offer valuable tools for understanding and depicting nonlinear physical phenomena.
- The methodology is extendable to a broader class of nonlinear partial differential equations.
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