Symmetry reductions and invariant-group solutions for a two-dimensional Kundu–Mukherjee–Naskar model

New Wave Solutions for the Two-Mode Caudrey–Dodd–Gibbon Equation

“…It is important to note that the existence of the dispersion is essential for finding soliton solutions [21,22]. The way of generating a twomode equation used here for CDG could be also applied to other NPDs, for example, the Eckhaus-Kundu equation [23] or the Kundu-Mukherjee-Naskar equation [24].…”

Bending of optical solitonic beams modeled by coupled KMN equation

“…Many kinds of solutions of the KMN equation were derived like higher-order rational solutions [16], optical dromions and domain walls [17,18], various optical soliton solutions having different features [19][20][21][22][23][24][25][26][27][28][29], and different analytic solutions [30][31][32][33][34][35][36][37], power series solutions [38], complex wave solutions [39,40], periodic solutions (via variational principle) [41], solitons in birefringent fiber system [42,43], etc. Integrable properties such as Lax pair, conservation laws, higher order soliton solutions via Hirota method, symmetry analysis, nonlinear self-adjointness property, etc of KMN equation have been explored in [10,13,25,40,44]. Time fractional KMN equation has been introduced in [45] to examine periodic properties.…”

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.…”