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Dynamical behavior of the optical traveling pulses for the resonant nonlinear Schrödinger equation with external periodic force

Department of Mathematics, University of Kalyani, Kalyani 741235, India

Corresponding author.

Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim 737136, India

E-mail Address: asit_saha123@rediffmail.com

E-mail Address: asitsaha125@gmail.com

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, and

Niladri Ghosh

Department of Mathematics, University of Kalyani, Kalyani 741235, India

E-mail Address: niladri.02mgf@gmail.com

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https://doi.org/10.1142/S0217979220502550Cited by:7 (Source: Crossref)

Abstract

Dynamical behavior of the optical traveling pulses for the resonant nonlinear Schrödinger (RNS) equation with external periodic force is studied. Using a complex transformation we obtain an unperturbed dynamical system for the RNS equation. Existence of periodic optical pulses, solitary optical pulses of dark and bright types, breaking optical pulses is dispensed using phase plane analysis of the unperturbed dynamical system. Introducing an external perturbation to the unperturbed dynamical system, quasiperiodicity and chaotic features of the nonlinear optical pulses for the perturbed dynamical system are studied by varying the resonance parameter (c) with special values of other system parameters through different computational tools, like time series plot, phase plot, sensitivity plot, Lyapunov exponent, and Poincare section. The resonance parameter (c) acts as a control parameter on qualitative transition of the nonlinear optical pulses for the perturbed dynamical system from quasiperiodic motion to chaotic motion.

Keywords:

PACS: 02.30.Oz, 05.45.-a, 05.90.+m

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