Physically significant solitary wave solutions to the space-time fractional Landau–Ginsburg–Higgs equation via three consistent methods - Zulqarnain, Rana Muhammad; Ma, Wen-Xiu; Mehdi, Khush Bukht; Siddique, Imran; Hassan, Ahmed M.; Askar, Sameh (Frontiers in Physics, 2023)
The Landau-Ginzburg-Higgs equation (LGHE) is a mathematical model used to describe nonlinear waves that exhibit weak scattering and long-range connections in the tropical and mid-latitude troposphere as interactions between equatorial waves and mid-latitude Rossby waves. This article studies the fractional Landau-Ginzburg-Higgs model, previously introduced in truncated M-fractional derivatives utilizing the (G'/G, 1/G) modified (G'/G^2) and new auxiliary equations methods. Using employed techniques, different solutions, including unknown parameters, are obtained in trigonometric, hyperbolic, and exponential functions. This study investigates how varying values of the fractional parameter affect the deeds of the solutions obtained for the given conditions. The predicted solutions, obtained under restricted conditions, are visualized through 2D, 3D, and contour plots using appropriate parameter values. The attained results are confirmed for the abovementioned equations using symbolic soft computations. Moreover, the outcomes confirm that the methods used in this study are effective mathematical tools for discovering exact solitary wave solutions to nonlinear models that are encountered in various areas of science and engineering.