The analysis of the traveling wave solutions of the Hirota-Ramani equation via the modified Kudryashov method

Aslı Alkan; Mehmet Kayalar; Hasan Bulut; Aslı Alkan; Mehmet Kayalar; Hasan Bulut

doi:10.3934/math.2025153

AIMS Mathematics

2025, Volume 10, Issue 2: 3291-3305. doi: 10.3934/math.2025153

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The analysis of the traveling wave solutions of the Hirota-Ramani equation via the modified Kudryashov method

1.
Department of Mathematics, Faculty of Science, Fırat University, Elazığ, Turkey
2.
Vocational School, Vocational High School, Erzincan Binali Yildirim University, Erzincan, Turkey
3.
Department of Mathematics and Informatics, Azerbaijan University, Baku, Azerbaijan

Received: 08 September 2024 Revised: 13 January 2025 Accepted: 20 January 2025 Published: 20 February 2025
MSC : 35A24, 35A99, 35C07

In this paper, the modified Kudryashov method is utilized to construct the exact traveling solutions to the Hirota-Ramani equation. The Hirota-Ramani equation holds significant importance as a fundamental model in the examination of nonlinear and integrable systems. It offers valuable theoretical insights and practical applications across multiple domains of physics and applied mathematics. The modified Kudryashov method was utilized to acquire the novel solutions of the Hirota-Ramani equation. Consequently, numerous analytical exact solutions have been derived, including rational, trigonometric, and hyperbolic function solutions. This method is potent, effective, and serves as an option for developing new solutions to many sorts of fractional differential equations utilized in mathematical physics.
- Kudryashov method,
- the Hirota-Ramani equation,
- traveling wave solution
Citation: Aslı Alkan, Mehmet Kayalar, Hasan Bulut. The analysis of the traveling wave solutions of the Hirota-Ramani equation via the modified Kudryashov method[J]. AIMS Mathematics, 2025, 10(2): 3291-3305. doi: 10.3934/math.2025153

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Abstract

In this paper, the modified Kudryashov method is utilized to construct the exact traveling solutions to the Hirota-Ramani equation. The Hirota-Ramani equation holds significant importance as a fundamental model in the examination of nonlinear and integrable systems. It offers valuable theoretical insights and practical applications across multiple domains of physics and applied mathematics. The modified Kudryashov method was utilized to acquire the novel solutions of the Hirota-Ramani equation. Consequently, numerous analytical exact solutions have been derived, including rational, trigonometric, and hyperbolic function solutions. This method is potent, effective, and serves as an option for developing new solutions to many sorts of fractional differential equations utilized in mathematical physics.

References

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