Document Type : Research Paper
Authors
1
1. School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya 47500, Selangor Darul Ehsan, Malaysia.\\ 2. Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh. \\ 3. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India.
2
1. School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya 47500, Selangor Darul Ehsan, Malaysia.\\ 2. Miyan Research Institute, International University of Business Agriculture and Technology, Dhaka 1230, Bangladesh.
3
School of Engineering and Natural Sciences, Istanbul Medipol University, 34810, Istanbul, Turkey.
4
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia.
Abstract
The integrable reduced spin Hirota-Maxwell-Bloch (rsHMB) equation is an important nonlinear equation, which models the femtosecond pulse propagation in spin-field coupling, erbium-doped fibre, fibre optic technologies, and magnetisation reversal effects. Despite its general applicability, a careful analytical study of the dynamical behaviour of the rsHMB equation, including bifurcation structures, chaotic evolution, and sensitivity to initial perturbations, remains lacking. To fill this gap, this paper obtains correct soliton solutions and examines the nonlinear dynamics of the equation of rsHMB. The bifurcation and sensitivity analysis of a dynamical system is used to study periodic, quasiperiodic, and chaotic behaviours. The Runge-Kutta technique is utilized to determine the stability of the system under minimal perturbations, and the modified extended tanh technique (METF) is used to obtain various types of soliton solutions. Anti-kink, v-shaped, and compact on waves are all examples of soliton structures that can be represented in various graphical displays, such as 2D, 3D, contour, density, and modeling profiles before rotation, as well as 3D rotating surfaces. The findings affirm the nonlinear complexity of the system’s nonlinear behaviour, exhibiting elastic soliton collisions, amplitude modulation, and energy conservation. The findings are part of the theoretical knowledge of ultrafast pulse propagation in erbium-doped fibres and provide valuable data for the improvement of biological imaging, optical communication, and magnetic data storage. This work will contribute to the development of nonlinear dynamical modeling and soliton-based applications in recent photonic technology and nonlinear science studies to a large extent.
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