Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation

Multiple Accurate-Cubic Optical Solitons to the Kerr-Low and Power-low Nonlinear Schrodinger Equation without the Chromatic Dispersion

“…In related subject the SWAM has been applied effectively to establish other new accurate perceptions of the cubic solitons for the kerr-law and power law nonlinearity mentioned before, which are obviously through Figures (17)(18)(19)(20)(21)(22)(23)(24)(25)(26). Our new achieved pictures of the accurate cubic soliton solutions in the framework of these two various manners which weren't achieved before by any other authors denote to the novelty of these results, especially compared with that achieved previously by [6][7][8] and [33][34] who applied different techniques to study these two cases significantly. Consequently, new distinct and impressive visions to the cubic solitons of these two different versions of this model have been demonstrated.…”

“…In the last few decades the dynamics of optical soliton cause surprise development in the telecommunications engineering [21][22][23][24][25][26][27][28][29][30][31][32]. Recently, few studies have been implemented to discuss the NLSE in the presence of the third order dispersion and absence of the chromatic dispersion [6][7][8], [33][34],while in the absence of third order dispersion and the chromatic dispersion this equation doesn't integrable [35]. According to [18], the suggested model can be proposed in the form,…”

Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

“…Solitons and solitary wave solutions of this model have recently been tried to be found by many researchers. Various methods have been studied such as the extended simple equation method and the exp (−ϕ(ξ))-expansion method (Lu et al, 2019), the generalized Riccati mapping method (Nasreen et al, 2019), the exp-a function and unified methods (Hosseini et al, 2020), F-expansion method (Seadawy et al, 2020b) and modified extended direct algebraic method (Seadawy et al, 2020a).…”

Exact Traveling Wave Solutions of the Gardner Equation by the Improved tanΘϑ-Expansion Method and the Wave Ansatz Method

“…Equation ( 1) is also called the combined KdV-mKdV equation. In recent years, partial differential equations have become one of the most widely used fields of mathematics in various branches of science and engineering [5][6][7][8][9][10][11][12]. In this paper, the Gardner equation is examined by using the improved tan(Θ(ϑ))-expansion method and the wave ansatz method.…”

“…In [25], the authors have studied the attitudes of some solitary solitons for this equation. Many powerful analytic solution methods for solving nonlinear equation (1) have appeared in the open literature, such as the Hirota bilinear method [26], mapping method [25], similarity transformation method [27], generalized exponential rational function method, Jacobi elliptical solution finder method [28], fractional homotopy perturbation transform method [29], Coffey's series expansion method [30], a unified method including solitary wave solutions, triangular periodic solutions, and Jacobi periodic wave solutions, as well as rational solutions [23], Wadati's inverse scattering transform and Hirota methods [31,32], consistent Riccati expansion (CRE) [33], planar dynamical systems approach method [34], Kudryashov method [35], Lie symmetry group method [36], ill-posedness results [37], classification of single traveling wave solutions [38], spectral collocation method [5], the Gardner equation with time-dependent coefficients and forcing term, have been investigated in [39,40]. For more methods, we refer the readers to [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and the references therein.…”