Dispersive optical soliton solutions of the generalized Radhakrishnan–Kundu–Lakshmanan dynamical equation with power law nonlinearity and its applications

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

“…(9). When we compare our results with the results reported in [40][41][42][43][44][45][46][47], we observed that, all the results obtained in this study by using the above method are newly structured solutions. These soliton solutions are located throughout parameter restrictions that provide their existence and novel soliton, traveling waves and kink-type solutions with complex structures while other solutions that emerged from the Laplace-Adomian decomposition method, traveling wave hypothesis, extended trial function scheme, among others.…”

“…For instance, in [40][41] the 1-soliton solutions of this equation are obtained by using solitary wave ansatz. New auxiliary equation method and extended simple equation method are two integration schemes used in [42] to carry out the integration of this model. The work of [43] is devoted to extract some optical soliton solutions to the model with Kerr and power laws of nonlinearity by means of extended trial function scheme.…”

On Highly Dimensional Elastic and Nonelastic Interaction between Internal Waves in Straight and Varying Cross-Section Channels

“…Depending on the potential of the nonlinear partial differential equation to describe several complicated processes in diverse fields such as physiology, plasma physics, hydrodynamics, fluid mechanics, and optics, numerous precise and computational schemes such as in [23][24][25][26] have been developed. Using inspired schemes, computational and technical advances are seen as the basic usefulness of solving these phenomena [27][28][29][30][31]. Such schemes have recently been regarded as simple methods for discovering the different formulas of moving wave solutions to these dynamic phenomena [32][33][34].…”

Optical solitons to the fractional Schrödinger-Hirota equation

“…Optical solitons are restrained electromagnetic waves that stretch in nonlinear dispersive media and allow the intensity to remain unchanged due to the balance between dispersion and nonlinearity effects [4]. Various analytical approaches for securing optical solitons and other solutions to different kind of NLSEs have been reported to the literature such as the the sine-Gordon expansion method [5][6][7], the first integral method [8,9], the improved Bernoulli sub-equation function method [10,11], the trial solution method [12,13], the new auxiliary equation method [14], the extended simple equation method [15], the solitary wave ansatz method [16], the functional variable method [17], the sub-equation method [18][19][20] and several others [21][22][23][24][25][26][27][28][29][30][31][32][33].…”