The chaotic, supernonlinear, periodic, quasiperiodic wave solutions and solitons with cascaded system

Abstract

In this research article, the dynamics of optical solitons in cascaded system with spatio-temporal dispersion is discussed. The Kerr medium is considered for this investigation. Two versatile integration tools have been used to extricate different traveling wave solutions. Rapid convergent approximation method has been employed to extract bright, singular and periodic solitons whereas polynomial function solutions are obtained by unified method. The constraints on the parameters for the validity of these solutions are also provided. Galilean transformation is prosecuted to construct the planer dynamical system of the said model. Runge–Kutta fourth-order technique is used to extract the non-linear periodic waves of the considered problem and consequences are depicted through different portraits. Further, by employing an extrinsic periodic force, chaotic and quasiperiodic pattern of discussed model is analyzed for different values of the parameters. While chaotic and quasiperiodic behaviors are observed for some values of parameters of considered system by keeping the force and frequency of the perturbed dynamical system fixed. Sensitive anatomy is carried out for diverse initial value problems. It is investigated that the chaotic and quasiperiodic pattern is present in the perturbed dynamical system.

Keywords:

• Chaos
• quasiperiodic
• supernonlinear waves
• solitons
• cascaded system
• rapid convergent approximation method
• the unified method

Disclosure statement

No potential conflict of interest was reported by the authors.