A hybrid analytical and numerical analysis of ultra-short pulse phase shifts

This study uses a simplified third-order generalized nonlinear Schrödinger equation (3-order GNLSE) to investigate the soliton phase shift. Most of the time, this model is used to explain what happens to ultrashort pulses in quantum environments and optical fibers. On the other hand, it could be used as a wave model to show how materials work acoustically. From a quantum-mechanical state function, it might be possible to figure out how atoms and transistors move and act in the real world. The novel the direct algebraic (NDA) method is employed to solve this model through constraining some novel solitary wave solutions. All assessed solutions are put through their paces using two state-of-the-art numeric methods (trigonometric quantic and cubic B–spline). The computational solutions meet all the conditions for creating numerical systems. Two–, three–, and contour diagrams show how analytical and numerical answers match up with the solutions. The comparison between our results and recently studies on this model, shows how our solutions are novel and accurate.