Exact soliton solutions and stability analysis to (3 + 1)-dimensional nonlinear Schrödinger model

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.