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

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. © 2025 the Author(s), licensee AIMS Press.