Optical solitons to the Kundu–Mukherjee–Naskar equation in (2+1)-dimensional form via two analytical techniques

Abstract

The current research is about the optical solitons of the Kundu–Mukherjee–Naskar (KMN) equation that are obtained by implementing the two proficient approaches named: the extended Jacobi’s elliptic expansion function method and the [Formula: see text] function method. The aforesaid methods are used for the first time in the KMN equation to obtain novel soliton solutions in terms of Jacobi’s elliptic function solutions, which turn into dark, bright, and periodic solutions later. Also, the rational function solutions of the above-mentioned equation are obtained. The obtained solutions are also graphed and verified with the use of symbolic soft computations. The obtained results may be applied to illustrate the substantial concept of the studious structures as well as other related nonlinear physical structures.

Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model

“…As a result, the researchers focused solely on obtaining bright, dark, and singular soliton solutions for an integer-order KMN model. Compared to the soliton solutions attained in previous studies [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], the bright, dark, periodic, and singular soliton wave solutions generated in this study are novel in terms of their use of the generalized fractional derivative. This approach has not been reported in previously published articles, to the best of the authors' knowledge.…”

“…A generalized fractional derivative is used. As mentioned earlier in the literature section, several researchers have reported diverse methods for obtaining bright, dark, and singular soliton solutions to integer-order KMN models [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. As a result, the researchers focused solely on obtaining bright, dark, and singular soliton solutions for an integer-order KMN model.…”

“…Onder et al [25] introduced optical soliton solutions for the KMN equation using the Sardar sub-equation and the new Kudryashov methods. Using the extended Jacobi's elliptic expansion function and the exp a function methods, Zafar et al [26] obtained novel soliton solutions for the KMN equation. Kumar et al [27] found dark, bright, periodic U-shaped, and singular soliton solutions for Equation (1) using the generalized Kudryashov and the new auxiliary equation methods.…”

Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques

“…There are several definitions of fractional derivatives such as Riemann Liouville [2], conformable fractional derivative [3], beta derivative [4], and new truncated M-fractional derivative [5] are available in literature. Many powerful methods for obtaining exact solutions of nonlinear fractional PDEs have been presented as Hirota's bilinear method [6], sinecosine method [7], tanh-function method [8], exponential rational function method [9], Kudryashov method [10], sine-Gordon expansion method [11], modified ðG ′ /GÞ -expansion method [12], extended ðG ′ /GÞ-expansion method [13], ðG ′ /GÞ-expansion method [14], tanh-coth expansion method [15], Jacobi elliptic function expansion method [16], first integral method [17], sardar-subequation method [18], new subequation method [19], extended direct algebraic method [20], exp ð−ϕðηÞÞ method [21], Exp a function method [22], ð1/G′Þ, ðG′/G, 1/GÞ, and modified ðG′/ G 2 Þ − expansion methods [23,24], Kudryashov method [25], modified expansion function method [26], new auxiliary equation method [27], extended Jacobi's elliptic expansion function method [28], extended sinh-Gordon equation expansion method [29], modified simplest equation method [30], and many more.…”