New exact solutions to the high dispersive cubic–quintic nonlinear Schrödinger equation

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

“…Finding the value of k and then inserting Equations (10) and (12) into Equation (9), we get a system of terms of:…”

“…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 specifically reported by Chiao et al [1] in their research of optical beams. In the past several years, various methods have been proposed to obtain the exact optical soliton solutions of the non-linear Schrödinger equation [2][3][4][5][6][7][8][9][10][11][12]. Dispersion and non-linearity are two of the essential components for the distribution of solitons across inter-continental regions.…”

High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions

“…In the present paper, the dispersive cubic-quintic Schrödinger equation (DCQSE) including higher-order time derivatives is studied through the exp a -function scheme. The nonlinear governing model in its dimensionless form is presented as below [25][26][27]:…”

“…The solitary wave solutions of the model (1) were also gained by Azzouzzi and her colleagues [26] by means of the complex envelope function approach. Xie and his co-workers [27] obtained distinct exact solutions of the model (1) using the complete discrimination system technique.…”

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

“…In recent years, many researchers have carried out investigations on the governing models in optical fibers. The nonlinear Schrödinger equation, involving cubic and quartic-order dispersion terms, has been investigated to seek the exact optical soliton solutions via the undetermined coefficients method [36], the modified Kudryashov approach [37], the complete discrimination system method [38], the generalized tanh function method [39], the sin-cosine method, as well as the Bernoulli equation approach [40], the semi-inverse variation method [41], a simple equation method [3], and the extended sinh-Gordon expansion method [42]. Now, optical solitons are the exciting research area of nonlinear optics studies, and this research field has led to tremendous advances in their extensive applications.…”