On the Dispersive Optical Pulses in Fiber Optics of the Conformable (2 + 1)-Dimensional Hirota–Maccari System

The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects. Therefore, the main goal of this work is to compile new soliton structures to the HM system in hyperbolic, trigonometric, exponential, and rational forms, both single and combined version, by using three robust analytical approaches: the new extended rational sinh-Gordon equation expansion method (ShGEEM), the G′/G,1/G-expansion method, and the new extended hyperbolic function method (EHFM). The solutions thus obtained are also tested for their validity and accuracy using Mathematica. In order to exhibit the physical properties of the soliton pulses, we depict 2D, 3D, and contour graphs by using suitable values of the parameters. These methods play a major role compared with other methods in the literature because new and more general solutions are obtained with additional free parameters. Remarkably, all the known solutions are special cases of our generalized solutions. An important feature of the proposed methods is their simplicity, robustness, and computational efficiency that can be widely extended to nonlinear partial differential equations in all scientific disciplines. The efficiency of this framework thus indicates at its application in addressing complicated problems in the future.