Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Abstract

This paper retrieves some new optical solutions to the Kundu-Mukherjee-Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, the generalized Kudryashov and new auxiliary equation methods are applied to the KMN equation and consequently, dark, bright, periodic U-shaped and singular soliton solutions are explored. The discrepancies between the present obtained solutions and the previously obtained solutions by using different methods are discussed. The time fractional derivative and an oblique wave transformation in coordination with the methods of interest are considered for acquiring new optical wave solutions of the KMN equation in the sense of conformable derivative and wave obliqueness, respectively. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. All the obtained optical solutions are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods. Finally, it is found that the utilized methods and the relevant transformation are powerful over the other methods and it can be applicable for further studies to explain the pragmatic phenomena in optical fiber communication systems.

Novel localized waves and interaction solutions for a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions

“…the modified Kudryshov method [20,21], the generalized Kudryashov method [22], the Jacobi elliptic function expansion method [23], the sine-Gordon expansion method [24], the extended sinh-Gordon expansion method [25][26][27], the ( / , 1/ )-expansion method [28], the auxiliary equation method [29], the new auxiliary equation method [22,30], the variable separation method [31], the Riemann-Hilbert space approach [7,32], the Painlevé analysis [33], the Consistent Riccati expansion method [34], and the HBM [3,9,[35][36][37][38].…”

New Optical Solitons in Bragg Grating Fibers for the Nonlinear Coupled ( 2 + 1 )-Dimensional Kundu-Mukherjee-Naskar System via Complete Discrimination System Method

“…In [4], Ekici et al indicated that the KMN equation is applicable to study the dynamics of soliton propagation through optical fibers in (2 + 1) dimensions on the bases of the fact that RWs are observed in a crystal fiber [5]. Note that the use of special methods constructing exact solutions of nonlinear differential models (see [6][7][8][9][10][11][12][13]) is a main research area of nonlinear optical science, the optical solitons in KMN equation have been addressed by broad researchers to recover the exact solutions by applying many effective methods including Kudryashov's approach method [14,15], the tanh function method [16], the new auxiliary equation method [17], the new extended direct algebraic method [18,19], the method of undetermined coefficients and Lie symmetry [20,21], the trial equation technique [22], the functional variable method [23], and the modified simple equation approach technique [24]. It is worth mentioning that Yldrm [25] also used the modified simple equation approach technique to discuss a new model of coupled KMN equations in birefringent fibers.…”

Traveling wave solutions for the generalized (2+1)-dimensional Kundu-Mukherjee-Naskar equation

“…In 2020, Rizvi [21] got dark, bright, periodic U-shaped and singular solitons through the generalized Kudryashov method. Subsequently, Kumar [22] discussed singular, dark, combined darksingular solitons and other hyperbolic solutions by using the csch method, extended tanh-coth method and extended rational sinh-cosh method. Meanwhile, Talarposhti [23] and Ghanbari [24] derived some new solitary solutions by using the Exp-function method.…”