W-shaped optical solitons of Chen–Lee–Liu equation by Laplace–Adomian decomposition method

Traveling Wave Solutions and Chaotic Motions for a Perturbed Nonlinear Schrödinger Equation with Power-Law Nonlinearity and Higher-Order Dispersions

“…Using the bifurcation analysis and qualitative theory, we analyze equilibrium points for system Eq. (30). We consider the following Jacobian matrix of system (30) at the equilibrium points X k , Y k ðÞ :…”

“…Although these equations explain the pulse dynamics in optical fibers [19][20][21][22], some of these nonlinear models are non-integrable. In this context, various computational and analytical methods have been proposed and used in the past few decades, to examine many classes of Schrödinger equation [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Nonetheless, these investigations reveal that the dynamic of solutions in non-integrable systems can be important and more complex.…”

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

“…Dark solitons are robust complex objects that have better stability (constant amplitude) against different disturbances compared to the bright solitons that are characterized by fiber loss, Raman effects, the mutual interaction between the adjacent pulses and the overlay of noise emitted by optical amplifiers, see [2] among others. More so, there are many various analytical and computational methods in the literature to address the class of Nonlinear Schrodinger Equations (NLSE) including among others [12][13][14][15][16][17][18][19][20][21][22][23] and the references therewith. Nevertheless, with regards to the CLL equation, very few computational techniques are available to numerically treat the model via the application of the standard Adomian's method and its modifications with particular types of soliton solutions [24][25][26][27][28][29].…”

“…However, the aim of this paper is to numerically study the CLL equation amidst the presence of dispersion and steepening terms via the applications of the Adomian Decomposition Method (ADM) and Improved Adomian Decomposition Method (IADM) [21][22][23]. Two types of optical soliton solutions comprising the dark and singular solitons are sought for as benchmark exact solitons for the validation of the proposed schemes.…”

Optical soliton perturbation of Fokas-Lenells equation by the Laplace-Adomian decomposition algorithm

“…One of the very many and modern numerical algorithms that will be implemented is the Laplace-Adomian decomposition integration scheme. This method has been successfully applied to variety of other models from optics [14][15][16]. This paper now studies FLE, for the first time, by the aid of Laplace-Adomian decomposition scheme.…”