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Introduction
Nonlinear evolution equations (NLEEs) are widely utilized mathematical models in numerous scientific disciplines, like, soliton theory, fluid mechanics, fiber optic communication, plasma physics, and quantum mechanics, where they are utilized to describe nonlinear phenomena [1, 2, 3–4]. With these equations, scientists can use the present state and governing dynamics of a system to predict its future states. Research can benefit decision-making, planning, and risk assessment by numerically or analytically solving these equations, which allow researchers to predict the behavior of physical, biological, or social systems under different settings. Climate modeling, environmental dynamics, and social dynamics are all big scientific concerns, and understanding emergent behavior is crucial for tackling them. In many branches of science, evolution equations play an essential role in forecasting, understanding, and controlling system dynamics, which in turn speeds up the development of new information, technologies, and creative ideas [5, 6, 7, 8–9].
So, exploring the exact solutions to NLEEs has emerged as a prominent subject of study in modern nonlinear science, capturing the interest of researchers from various disciplines including engineering, physics, and mathematics. In past decades, a succession of scientifically sound techniques for solving NLEEs have been developed, such that, the Darboux transformation (DT) [10], improved Bernoulli sub-equation function method [11], the inverse scattering transformation(IST) [12], the Hirota bilinear method [13], auxiliary equation method [14], generalized Kudryashov method [15], the tanh-function method [16], the exp-function method [17], the Adomian decomposition method [18], -expansion method [19], new extended direct algebraic method and new mapping method [20, 21], Sine-Gordon equation expansion method [22], modified Sardar sub-equation method [23], Lie symmetry technique [24], Bäcklund transformations [25] and [26, 27–28]. Ryogo Hirota initially proposed the Hirota bilinear method [29], and it has strong properties for solving nonlinear evolution equations involving nonlinear dispersion and dissipation effects. The Hirota method is the most effective tool for finding soliton solutions to nonlinear integrable systems. Transforming an equation into its bilinear form is the initial stage in solving a system using the Hirota method. Obtaining the bilinear form of a nonlinear system allows one to construct its soliton and multisoliton solutions. A lot of researchers are interested in the Hirota bilinear method because it works so well for studying the integrability of nonlinear scientific models...