Bifurcation study and pattern formation analysis of a nonlinear dynamical system for chaotic behavior in traveling wave solution

The behaviors of optical solitons with spatio-temporal dispersion of the nonlinear Schrodinger's equation with Kerr medium is discussed by using diverse integration technique. The tanh method is used to obtain the dark and bright, kink and anti-kink optical soliton, single and periodic solitons, and V-shape soliton. Furthermore, necessary as well as sufficient conditions for the formation of the solutions are also reported. Moreover, the planer dynamical system of the discussed equation is constructed using Galilean transformation and all possible phase portraits are presented and sensitive inspection is applied to check the sensitivity of the considered equation. Moreover, after adding perturbed term the chaotic and quasi-periodic behaviors have been observed for different values of parameters and multistability is reported at the end.