Abstract
In this manuscript, the optical solitons of nonlinear Schrodinger equation (NLSE) with cubic-quintic law nonlinearity, in the presence of self-frequency shift and self-steepening, has been studied. The ultrahigh capacity propagation and transit of laser light pulses in optical fibres were described using this form of equation. To extract new results, two strong methodologies has been used. To extract the exact solution unified method has been employed. The solutions obtained by this analytical method, are in form of polynomial and rational function solution. Moreover, the validity of non-singular solutions has guaranteed by a limitation condition that is graphically illustrated in 3D. The 2D graphical representation are also used to demonstrate the influence of parameters on the predicted non-singular solutions. The other technique, used for qualitative analysis, is bifurcation. The system has been transformed into a planer dynamical system, which has been transformed into a hamiltonian system. All the possible phase portrait has been plotted by complete discrimination method. The acquired results are novel and have not been recorded before and they indicate that the proposed methodologies may be used to investigate innovative soliton solutions and phase portraits for any NLSE.