Bifurcation analysis and the modulation instability in a nonlinear silica optical fibers
The Schafer-Wayne equation (SWE), a crucial model for ultrashort pulse propagation in nonlinear silicon optical fibers, is investigated using the F-expansion method and enhanced modified extended tanh expansion method (EMETEM). We derive diverse solitary wave solutions, including dark, bright, periodic, multi-peak periodic, and breather-like periodic solutions, visualized through 2D and 3D graphics. Novel contributions include comprehensive bifurcation analysis via planar dynamical systems revealing phase portrait classifications, modulation instability analysis for solution stability evaluation, and sensitivity analysis assessing parameter dependence and initial condition effects. The diverse solitary wave solutions represent a new advancement in understanding SWE dynamics. The study demonstrates the methods' robustness in examining nonlinear wave dynamics with applications in optics, engineering, and telecommunications.
In this study, we investigate the fractional telegraph equation, a key nonlinear model for signal transmission, wave propagation, and complex dynamical systems in engineering.
A key research challenge in modern cryptography is the construction of robust nonlinear components that simultaneously achieve high nonlinearity, resistance to linear and differential…
In this paper, we investigated higher-order smooth positon and breather-positon solutions of the Kuralay equation. Starting from the associated Lax pair, we constructed an explicit N-fold Darboux…