Various exact analytical solutions of some nonlinear partial differential equations

In this study, an analytical investigation of certain nonlinear partial differential equations in optical fibers is conducted. These equations consist of three different concatenation models: A model that combines the nonlinear Schrödinger equation, the LakshmananPorsezian-Daniel model, and the Sasa-Satsuma equation; a model characterized by the inclusion of the Kerr law of nonlinearity in birefringent fibers, and a model that incorporates the Kerr law of nonlinearity in the presence of spatio-temporal dispersion, Hamiltonian-type perturbation terms, and multiplicative white noise. The Cole-Hopf transformation and direct assumptions with arbitrary functions are utilized to determine several analytic solutions to the governing equations, including multi-wave solutions, two solitary wave solutions, breather waves, periodic cross kink solutions, Peregrine-like rational solutions, and three-wave solutions. The parameter constraints that serve as the requisite condition for the existence of these wave solutions are also identified. To explore and demonstrate the influence of different parameters on the interaction of some solutions reported in this research, 3D graphics and their corresponding contour plots are provided to vividly display these transmission and interaction characteristics. Results of this study may be useful for the experimental realization of certain nonlinear waves in optical fibers and further understanding of their propagation dynamics. Keywords: Multi-wave solutions, Breather waves, Periodic cross kink solutions, Peregrine-like rational solutions, Concatenation model, Multiplicative white noise, Birefringent fibers, Cole-Hopf transformation