Huda Daefallh Alrashdi

In the present research, we explored the various kinds of optical solitons and many other solitary wave solutions for the nonlinear Akbota equation by utilizing the symbolic computational simulation on the basis of the improved F-expansion approach. The nonlinear Akbota equation has applications in physics and engineering. The examined solitary wave and soliton solutions have interesting physical structures, including anti-kink wave solitons, bright solitons, kink wave solitons, dark solitons, periodic wave solitons, peakon bright solitons, peakon dark solitons, mixed bright–dark periodic solitons, mixed solitons in bright–dark form, and solitary wave structures. The newly extracted soliton solutions in this study shed light on the fact that the utilized approach is more efficient, concise, powerful, effective, straightforward, and simple, and we can also utilize it for other higher order nonlinear complex models. The extracted solutions will be helpful to understand the nonlinear phenomena in various areas of nonlinear sciences and engineering, including quantum physics, laser optics, nonlinear optics, optical fibers, ocean engineering, and electronic engineering. The physical interpretation of the extracted solutions is visualized in two-dimensional, three-dimensional, and contour graphics based on numerical simulation by using the computer software Mathematica. The presented research will be helpful for further investigation of analytical solitary wave and soliton solutions to the complex, higher order nonlinear evolution equations.

Abstract This work examined solitary wave solutions to the nonlinear damped Korteweg–de Vries equation by employing the new auxiliary equation approach. The physical structure to the secured solutions visualized in dark solitons, bright solitons, periodic solitons, kink and anti-kink wave solitons, peakon bright and dark solitons, and dispersive solitary waves. The physical interpretation of constructed solutions is visually portrayed using two-dimensional, three-dimensional, and contour plots on the basis of numerical simulation, which help comprehend the physical features of nonlinear behaviour for the solitary waves. The explored solutions will be play important role in Mathematical physics, ion-acoustic waves, dust-acoustic waves, and plasma physics. This study has demonstrated that our suggested method is more beneficial, successful, strong and effective for studying analytically various nonlinear partial differential equations (NLPDEs) that arise in mathematical physics, engineering, plasma physics, and many other scientific fields.