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The stochastic generalized nonlinear Schrödinger equation (SGNLSE) of third order in the Stratonovich sense is examined here. New elliptic, hyperbolic, trigonometric, and rational stochastic solutions are obtained using a modified mapping method. Because the GNLSE is extensively used in nonlinear optical phenomena, optical fiber communication systems, communication and heat pulse propagation in materials, the obtained solutions may be used to study a broad range of relevant physical phenomena. In order to interpret the effects of multiplicative noise, the dynamic performances of the various obtained solutions are displayed utilizing 3-D and 2-D graphs. We infer that multiplicative noise impacts and stabilizes the behavior of SGNLSE solutions. [ABSTRACT FROM AUTHOR]

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics. [ABSTRACT FROM AUTHOR]

The optical fiber communication system is one of the components of a supporting system in the modern Internet fields. Under investigation in this paper is a coupled fourth-order nonlinear Schrödinger system, which describes the ultrashort optical pluses in a birefringent optical fiber. By virtue of the existing Lax pair, generalized Darboux transformation, two- and three-soliton solutions are derived, with respect to the polarization components of the electric field. Based on such solutions, we graphically display (1) the elastic interactions between/among the two/three solitons on a zero-intensity background, where amplitudes of the solitons remain unchanged; (2) the inelastic interactions between/among the two/three solitons, where amplitudes of the solitons change; (3) the bound state among the three solitons; (4) the higher-order linear and nonlinear effects, represented by β , on the polarization components of the electric field: The interval between two peaks becomes smaller and the numbers of the peaks increase when the value of β increases; The three solitons move along the positive time direction when the value of β decreases; The distances between the adjacent peaks become smaller when the value of β increases. [ABSTRACT FROM AUTHOR]