Lie symmetry analysis for cubic–quartic nonlinear Schrödinger's equation

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

“…The first one is the ESEM which has a successful history in extracting the optical soliton solutions for many nonlinear phenomenas arising in different branches of science. This schema is applied perfectly to introduce new impressive and accurate visions of the cubic solitons for the Kerr-law and Power-law NLSE that involve the third-order dispersion effect and exclude the chromatic dispersion effect, which are obviously through Figures (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16). 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).…”

“…The arising problem for pure-quartic soliton related to the governing nonlinear Schrödinger equation can be nonintegrable one, for this reason we will propose the concept of cubic-quartic solitons in which the chromatic dispersion is replaced by the third order dispersion and fourth order dispersion together [5][6][7][8][9][10][11]. Specially, many studies in terms of various methods have been demonstrated through significant published articles that were extracted via many authors who discussed various forms of the cubic-quartic NLSE [11][12][13][14][15][16][17][18][19][20]. 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].…”

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

“…The exact solutions of Equation (12) may be given as sinh ( θ ) = ± csch (ζ ) or sinh ( θ ) = ± isech (ζ ) , (13) and cosh (θ ) = ± coth (ζ ) or cosh (θ ) = ± tanh (ζ ) . (14) Letting solutions of Equation (10) along with Equations (13) and (14) as the form…”

“…In fact it might happen that the GVD is tiny and thus totally ignored, in this case the dispersion effect is determined by third and fourth order dispersion effects. Subsequently, this equation has been studied in a variety of ways, such as the Lie symmetry [13], both the m + G ′ G -improved expansion, and the exp (−ϕ (ξ )) −expansion methods [14], and the semiinverse variation principle method [4]. In this study, the extended sinh-Gordon expansion method (ShGEM) is applied to the non-linear cubic-quartic Schrödinger equations with the Parabolic law of fractional order, which is given by…”

Optical Soliton Solutions of the Cubic-Quartic Nonlinear Schrödinger and Resonant Nonlinear Schrödinger Equation with the Parabolic Law

“…This term was implemented in 2017 for the first time. This model was later extensively researched through different points of view such as the semi-inverse variation principle [41], Lie symmetry [44], conservation rules [45], and the system of undetermined coefficients [37]. Consider the nonlinear Schrödinger and resonant nonlinear Schrödinger equations in the appearance of 3OD and 4OD without both GVD and disturbance.…”