New optical solitons of conformable resonant nonlinear Schrödinger’s equation

Abstract

Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrödinger’s equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.

Analytical solutions of (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method

“…Three-dimensional and contour plots of v 4 (x, y, t) are The method used in this article has been recently presented [39] and it produces various kind of solitons. As compared to existing methods in the literature, it is more easily applicable than the many methods such as G G ¢ ( )-expansion [40], projective Riccati equations [41], hyperbolic function [42,43] and Sardar sub-ODE [44,45] in the literature.…”

Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity

“…Over the last several decades, one of the most significant challenges has been the development of new methods to construct exact solutions for NLPD equations. In recent years, several new, more powerful, and effective approaches have been established to retrieve exact solutions of NLPD equations, the sine-Gordon expansion method [1][2][3][4], the (𝐺 ′ 𝐺 ⁄ )-expansion method [5][6][7][8], the Sardar sub-equation method [9][10][11][12], the Kudryashov method [13][14][15][16][17][18], and the exponential method [19][20][21][22][23][24][25], are examples to mention.…”

Diverse Soliton Structures of the ( 2 + 1 )-Dimensional Nonlinear Electrical Transmission Line Equation

“…The study of their soliton solutions is of great significance since they can make us more deeply understand the natural phenomena and their internal relations. So far, there are many effective methods available for constructing the soliton solutions such as the exp-function method [1][2][3][4], tanh-function method [5][6][7][8][9], (G′/G)-expansion method [10][11][12], F-expansion method [13,14], extended rational sine-cosine and sinh-cosh methods [15][16][17][18], Sardar-subequation method [19][20][21], and Sine-Gordon expansion method [22,23] [ [24][25][26][27][28][29][30][31]. In the current work, we aim to study the (2 + 1)-dimensional NETLE, which is expressed by [32] ∂ 2 ∂t 2 u − αu 2…”