Approximate Solutions for Dark and Singular Optical Solitons of Chen-Lee-Liu Model by Adomian-based Methods

Abstract

The current manuscript investigates by proposing new numerical schemes based on the Adomian's technique for the resolution of the dark and singular solutions of the Chen-Lee-Liu (CLL) equation. More precisely, the schemes are derived from the Wazwaz's modification of the Adomian's method and the improved Adomian's method for treating complex-valued evolution equations. The CLL model is applicable to a variety of applications including photonic and optical crystal fibers. The schemes which are implemented via the help of the Maple software have many salient advantages as contained in the comparative analysis. Finally, we depict certain results graphically together with some supportive tables, in addition to some comprehensive remarks.

Assorted optical soliton solutions of the nonlinear fractional model in optical fibers possessing beta derivative

“…Besides, optical soliton solutions of this model serve as the fundamental basis for modern telecommunication systems. In the previous literature, the CLL model has been examined through various methods, namely the Riccati-and generalized Bernoulli sub-ODE approaches, and the generalized tanh technique [40], the modified extended tanh expansion scheme [41], the formulation of coupled amplitude-phase [42], the extended trial equation scheme [43], the approaches of extended sinh-Gordon equation expansion, the logarithmic transformation and the ansatz approaches [44], the Lie symmetry technique [45], the Laplace-Adomian decomposition method [46], the trial equation technique [47], the MSE approach [48], the Adomian-based method [49], the improved Adomian decomposition method [50], the extended simplest equation process [51], the new extended hyperbolic function method [52], the trial equation method [53], the bifurcation technique [54], and others.…”