Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity

Abstract In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schrödinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponential function combinations are applied to construct the wave solutions. The accuracy of the derived solitons is validated through symbolic computations performed in Wolfram Mathematica, accompanied by graphical visualizations of the proposed solutions. The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. Additionally, introducing perturbed terms is examined, revealing chaotic patterns in the system. The impact of variations in amplitude and frequency parameters on the system’s dynamical behaviour is thoroughly investigated. The findings underscore the efficiency and reliability of the applied techniques, demonstrating their applicability to a wide range of complex nonlinear systems

Sub pico-second pulses in mono-mode optical fibers with Triki-Biswas model

Abstract This study explores the Triki-Biswas (TB) model, a novel model describing soliton dynamics in monomodal optical fibers with non-Kerr dispersion, to obtain optical solitons. Optical bright and singular solitons were derived using the generalized Jacobi elliptic function (gJEF) method and the $$\tan \left( \frac{V(\eta )}{2}\right) -$$ expansion method. Trigonometric, hyperbolic, exponential, polynomial, and rational functions are obtained. The physical dynamics of the obtained solutions confirmed the existence of known complex structures, such as shock waves, dark solitons, periodic waves, and singular periodic solutions. The simulations generated in Mathematica 11.3 are graphically presented to depict the nature of the acquired solutions. These results are novel and have not been reported previously in the literature