A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

Manzoor, Z.; Iqbal, Muhammad Sajid; Hussain, Shabbir; Ashraf, Fareeha; Inc, Mustafa; Tarar, Muhammad Akhtar; Momani, Shaher

doi:10.1007/s11082-023-04934-2

Opt Quant Electron

2023

DOI: 10.1007/s11082-023-04934-2

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A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

Z. Manzoor

Muhammad Sajid Iqbal

Shabbir Hussain

et al.

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2024

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Cited by 2 publications

References 41 publications

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Dynamics of several optical soliton solutions of a (3+1)-dimensional nonlinear Schrödinger equation with parabolic law in optical fibers

Kumar,

Kukkar

2024

Mod. Phys. Lett. B

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In this paper, we address various optical soliton solutions and demonstrate the different dynamics of solitary waves to a (3+1)-dimensional nonlinear Schrödinger equation (NLSE) with parabolic law (NLSE) using a newly created powerful and effective method named as the extended generalized Riccati equation mapping method. This technique presents an organized manner to reveal the essential dynamics. There is great significance of the nonlinear Schrödinger equations and their several formulations in numerous fields of science, particularly in nonlinear optics, optical fibers, quantum electronics, and plasma physics. Through the use of numerical simulations and mathematical analysis, we explore the characteristics and behavior of these solitary wave solutions in a variety of scientific contexts. These results demonstrate the essential complexity of the governing equation and yield novel derived solutions. These solutions contribute to a better understanding of nonlinear wave phenomena by highlighting the fundamental dynamics establishing solitary waves in the NLSE. To enhance our wider knowledge, we provide effective graphic representations of the nonlinear wave structures in the derived solutions utilizing a variety of graphs, including 3D, 2D, and density plots. Moreover, a specific transformation has been applied to transform the system into a planar dynamical system, and several phase portraits have been presented to examine its behavior. Furthermore, upon introducing a perturbed term, chaotic behavior has been observed across different parameter values through both two-dimensional and three-dimensional graphics.

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Dynamics of several optical soliton solutions of a (3+1)-dimensional nonlinear Schrödinger equation with parabolic law in optical fibers

Kumar,

Kukkar

2024

Mod. Phys. Lett. B

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A New Adaptive Levenberg–Marquardt Method for Nonlinear Equations and Its Convergence Rate under the Hölderian Local Error Bound Condition

Han,

Rui

2024

Symmetry

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The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective.

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A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

Cited by 2 publications

References 41 publications

Dynamics of several optical soliton solutions of a (3+1)-dimensional nonlinear Schrödinger equation with parabolic law in optical fibers

Dynamics of several optical soliton solutions of a (3+1)-dimensional nonlinear Schrödinger equation with parabolic law in optical fibers

A New Adaptive Levenberg–Marquardt Method for Nonlinear Equations and Its Convergence Rate under the Hölderian Local Error Bound Condition

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