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

Abstract

The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger 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 non-linear 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.

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

“…Arbitrary -solutions play a dominant role in non-relativistic quantum mechanics since the wave function and associated eigenvalues contain all the necessary information for a full description of a quantum system [5][6][7][8]. With the experimental verification of the Schrödinger equation, researchers have devoted much interest in solving the radial Schrödinger equation to obtain bound state solutions with various methods for some potential models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Quiescent Optical Solitons with Cubic–Quartic and Generalized Cubic–Quartic Nonlinearity

“…The governing model is the nonlinear Schrödinger's equation (NLSE) with CQ form of SPM [16][17][18] and the generalized CQ form of SPM, both with nonlinear CD. It must be noted that the governing NLSE with nonlinear CD and CQ form of SPM has been studied in the past by the aid of extended Jacobi's elliptic function approach [7].…”

Analytical Solutions of the Schrödinger Equation with Kratzer-screened Coulomb Potential for a Quarkonium System

“…where a , b and c are potential strength parameters. The Kratzer potential has been used as a potential model to describe inter-nuclear vibration of diatomic molecules by different authors [35,36]. Another potential model used significantly in nuclear, particle and condensed matter physics is the screened Coulomb potential, also known as Yukawa potential [37].…”