M. B. Almatrafi, Abdulghani Alharbi^*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.1, pp. 827-841, 2023, DOI:10.32604/cmes.2023.027344

Abstract The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics, physics, and engineering disciplines. This article intends to analyze several traveling wave solutions for the modified regularized long-wave (MRLW) equation using several approaches, namely, the generalized algebraic method, the Jacobian elliptic functions technique, and the improved Q-expansion strategy. We successfully obtain analytical solutions consisting of rational, trigonometric, and hyperbolic structures. The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation. The adaptive moving mesh method evenly distributes the points on the high error areas. This method perfectly and… More >

Fahad Sameer Alshammari¹, Md Fazlul Hoque², Harun-Or-Roshid², Muhammad Nadeem^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2197-2217, 2023, DOI:10.32604/cmes.2023.022301

Abstract We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the… More >

Yuming Chu^1,2, Muhannad A. Shallal³, Seyed Mehdi Mirhosseini-Alizamini⁴, Hadi Rezazadeh⁵, Shumaila Javeed^6,*, Dumitru Baleanu^7,8

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1369-1378, 2021, DOI:10.32604/cmc.2020.012611

Abstract The purpose of this work is to find new soliton solutions of the complex Ginzburg–Landau equation (GLE) with Kerr law non-linearity. The considered equation is an imperative nonlinear partial differential equation (PDE) in the field of physics. The applications of complex GLE can be found in optics, plasma and other related fields. The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE. The results are presented under a suitable choice for the values of parameters. Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real, and imaginary… More >