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All Journal Vokasi UNESA Bulletin of Engineering, Technology and Applied Science
Jibrin Sale Yusuf
Federal University Duste
Computer Science & IT Engineering Mechanical Engineering Transportation

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Exact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method Jibrin Sale Yusuf
Vokasi UNESA Bulletin of Engineering, Technology and Applied Science Vol. 1 No. 3 (2024)
Publisher : Universitas Negeri Surabaya or The State University of Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/vubeta.v1i3.35831

Abstract

The propagation of optical pulses in nonlinear media is a complex phenomenon that requires accurate modeling and analysis. The New Hamiltonian Amplitude Equation (HNLS) is a fundamental model that describes this phenomenon, but solving it exactly is a challenging task. We employ the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. This research contributes to the understanding of optical soliton dynamics in various nonlinear regimes, providing a foundation for the development of novel optical communication systems and devices. We use the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. The method is applied to various nonlinear regimes, including Kerr law, Quadratic Cubic, and Parabolic law nonlinearities. Additionally, we obtain particular solutions using the power series method. The resulting optical soliton solutions are expressed in terms of various mathematical functions, including trigonometric functions, hyperbolic functions, exponential functions, and rational functions. These solutions describe the oscillatory behavior, exponential growth or decay, rapid growth or decay, and algebraic decay or growth of optical pulses in various nonlinear regimes. The solutions obtained using the power series method provide further insight into the behavior of optical pulses in these regimes. Our results provide a comprehensive understanding of optical soliton dynamics in nonlinear media
Investigating Soliton-Wave Dynamics Using the Focusing Nonlinear Schr¨odinger Equation Jibrin Sale Yusuf
Vokasi UNESA Bulletin of Engineering, Technology and Applied Science Vol. 3 No. 1 (2026)
Publisher : Universitas Negeri Surabaya or The State University of Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/vubeta.v3i1.43039

Abstract

This research undertakes a comprehensive investigation of the optical soliton solutions of the Focusing Non- linear Schr¨odinger Equation (NLSE), a fundamental model describing the propagation of optical solitons in nonlinear media. We employ two versatile and efficient methods: the Ricatti-Bernoulli Sub Ordinary Differential Equation (RBSODE) method and the Bernoulli Sub Ordinary Differential Equation (BSODE) method. These methods enable us to derive a wide range of optical soliton solutions. We examine two distinct nonlinearities: the Kerr law nonlinearity and the quadratic-cubic nonlinearity. These nonlinearities are crucial in determining the behavior of optical solitons in various nonlinear optical media. Our analysis reveals that the derived soliton solutions exhibit distinct characteristics. Kerr nonlinearity supports sharper, narrower solitons, whereas quadratic-cubic nonlinearity yields broader profiles with enhanced stability. This study obtains soliton solutions of the NLSE with Kerr and QC nonlinearities using the RBSODE and BSODE methods, analyzes the qualitative differences in the obtained profiles, and examines the conservation laws characterizing the dynamics. The RBSODE and BSODE methods are chosen for their algebraic flexibility and their ability to handle the nonlinearODEs derived from the traveling-wave reduction of the NLSE. Furthermore, we use the multiplier method to derive the conservation laws of the NLSE. These conservation laws provide valuable insights into the underlying dynamics of the optical solitons and have significant implications for the design and optimization of nonlinear optical systems. Our research contributes to the understanding of soliton behavior in nonlinear media, with potential applications in optical signal transmission and ultrafast laser propagation.
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