A Variety of Optical Soliton Solutions of DNLSE via Complete Discrimination System for Polynomial Method - Rizvi, Syed Tahir Raza; Ali, Kashif; Aziz, Noor; Seadawy, Aly. R. (Journal of Applied Nonlinear Dynamics, 2026)
The aim of this research is to demonstrate that bifurcation, topological properties and critical conditions of nonlinear dynamics can be clearly understood using complete discrimination system for polynomial method (CDSPM). Our conclusion is supported by an example of derivative nonlinear Schrödinger equation (DNLSE) with quintic nonlinearity, which describes how femtosecond pulses travel across nonlinear optical fibre. The results show that CDSPM is not only implemented to achieve the quantitative results such as classification of travelling waves, but also to carry out qualitative analysis of nonlinear differential equations. Jacobian elliptic solutions, hyperbolic function solutions, rational solutions are a few of the optical soliton solutions of DNLSE that are obtained by CDSPM. The qualitative analysis highlights the equilibrium points and the phase portraits of the system. Phase portraits are graphical representations applied in dynamical structures to depict the periodic behavior and the stability of the system. Our findings have broad applications in nonlinear optics, communication physics and other related domains. These chirps either amplify or compress the wave signals in optical fibers and nonlinear electrical transmission lines. The newly discovered chirped soliton solutions of DNLSE are useful in comprehending phenomena when waves are controlled by this kind of equation.