Bifurcation analysis and new exact complex solutions for the nonlinear Schrödinger equations with cubic nonlinearity

Nonlinear Schrödinger equations with cubic nonlinearity are a model of wave propagation in fiber optics and have numerous nonlinear effects in four-wave mixing, ultrashort pulses, second-harmonic generation, self-phase modulation, stimulated raman scattering, etc. In this study, we apply the modified \((G'/G)\)-expansion scheme to the Nonlinear Schrödinger equations with cubic nonlinearity in order to obtain numerous new exact complex wave solutions and their Bifurcation analyses. Despite the fact that numerous new exact complex wave solutions and bifurcation analyses had previously been determined for Nonlinear Schrödinger equations with cubic nonlinearity by a number of researchers, this study yielded not only more precise wave solutions but also new exact complex wave solutions and their Bifurcation analyses.Wave propagation in soliton physics, modulus instability in plasma physics, and soliton propagation in optical fibers may be better understood with the acquired information. To examine the nonlinear effects of the Nonlinear Schrödinger equations with cubic nonlinearity, 2D, 3D, contour, and BA diagrams are created. The Hamiltonian function is established to further the analysis of the phase plane’s dynamics. The simulations were conducted using Python and MAPLE software tools. Therefore, the modified \((G'/G)\)-expansion scheme solution procedure is more straightforward than other conventional methods.