Certain analytical solutions of the concatenation model with a multiplicative white noise in optical fibers

Abstract

In the presence of spatio-temporal dispersion, perturbation terms of the Hamiltonian type as well as multiplicative white noise, analytical investigation of the concatenation model having the Kerr law of nonlinearity is carried out in this work. The Cole–Hopf transformation and direct assumptions with arbitrary functions are utilized to determine several analytic solutions to the governing equation, including multi-wave, two solitary wave, breather, periodic cross kink, Peregrine-like rational, and three-wave solutions. The parameter constraints that serve as the requisite condition for the existence of these wave solutions are also identified. In order to explore and illustrate the propagation and dynamical behaviors of some solutions reported in this research, 3D graphics and their corresponding contour plots are included. Results of this paper may be useful for the experimental realization of certain nonlinear waves in optical fibers and further understanding of their propagation dynamics.

Novel highly dispersive soliton solutions in couplers for optical metamaterials: leveraging generalized Kudryashov’s Law of refractive index with eighth-order dispersion and multiplicative white noise

“…When l 0 = l 1 = l 3 = 0, the outcome is as follows: via the restrictions under the condition that a 18 c 18 < 0. By substituting (28) with the established solutions of equation (26) cited in [3] into (27) and incorporating (22), (3), and (4), we can derive two distinct types of soliton solutions as outlined below:…”

“…V.If l 0 > 0, the solutions are expressed in terms of WEFs: and under the condition that a 18 c 18 < 0. By substituting (60) with the established solutions of equation (26) cited in [3] into (27) and incorporating (22), (3), and (4), four varieties of soliton solutions can be obtained, each contingent upon different selections of l 0 , l 2 , and l 4 , as detailed below:…”

“…The integration of optical metamaterials into the study of solitons represents a promising avenue for advancing the capabilities of optical communication networks and devices [19,20]. By harnessing the synergistic potential of solitons and metamaterials, researchers aim to unlock new frontiers in optical communications, paving the way for enhanced data transfer rates, greater bandwidth utilization, and improved overall network efficiency [21,22].…”

“…under the same constraints(29), assuming a 18 c 18 < 0. By substituting (74) with the established solutions of equation(26) referenced in[3] into(27) and incorporating(22), (3), and (4), the resulting solutions are the straddled solitons:…”