Abstract
The research paper aims to investigate the space-time fractional cubic-quartic nonlinear Schrodinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the nonlinear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.
Highlights
AND MOTIVATIONNon-linear partial differential equations have different types of equations, one of them is the non-linear Schrödinger equation (NLSE) that relevant to the classical and quantum mechanics.The non-linear Schrödinger equation is a generalized (1+1)-dimensional version of the Ginzburg-Landau equation presented in 1950 in their study on supraconductivity and has been reported by Chiao et al [1] in their research of optical beams
It might happen that the group velocity dispersion (GVD) is tiny and totally ignored, in this case the dispersion effect is determined by third and fourth order dispersion effects
This equation has been studied in a variety of ways, such as the Lie symmetry [13], both the m
Summary
Non-linear partial differential equations have different types of equations, one of them is the non-linear Schrödinger equation (NLSE) that relevant to the classical and quantum mechanics. It might happen that the GVD is tiny and totally ignored, in this case the dispersion effect is determined by third and fourth order dispersion effects This equation has been studied in a variety of ways, such as the Lie symmetry [13], both the m. 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 iDαt u + iβD3xαu + γ D4xαu + cF |u|2 u = 0,. F (u) = c1u + c2u2, on Equation (1), we obtain the fractional non-linear Schrödinger equations with Parabolic law as follows: iDαt u + iβD3xαu + γ D4xαu + c1|u|2 + c2|u|4 u = 0.
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