Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Md Nur Hossain, Faisal Alsharif, M. Mamun Miah () and Mohammad Kanan ()
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Md Nur Hossain: Graduate School of Engineering, Osaka University, Suita 565-0871, Osaka, Japan
Faisal Alsharif: Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 30002, Saudi Arabia
M. Mamun Miah: Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh
Mohammad Kanan: Department of Industrial Engineering, College of Engineering, University of Business and Technology, Jeddah 21448, Saudi Arabia

Mathematics, 2024, vol. 12, issue 10, 1-19

Abstract: This study extensively explores the Biswas–Milovic equation (BME) with Kerr and power law nonlinearity to extract the unique characteristics of optical soliton solutions. These optical soliton solutions have different applications in the field of precision in optical switching, applications in waveguide design, exploration of nonlinear optical effects, imaging precision, reduced intensity fluctuations, suitability for optical signal processing in optical physics, etc. Through the powerful ( G ′ / G , 1 / G )-expansion analytical method, a variety of soliton solutions are expressed in three distinct forms: trigonometric, hyperbolic, and rational expressions. Rigorous validation using Mathematica software ensures precision, while dynamic visual representations vividly portray various soliton patterns such as kink, anti-kink, singular soliton, hyperbolic, dark soliton, and periodic bright soliton solutions. Indeed, a sensitivity analysis was conducted to assess how changes in parameters affect the exact solutions, aiding in the understanding of system behavior and informing decision-making, especially in accurately designing or analyzing real-world optical phenomena. This investigation reveals the significant influence of parameters λ , τ , c , B , and Κ on the precise solutions in Kerr and power law nonlinearities within the BME. Notably, parameter λ exhibits consistently high sensitivity across all scenarios, while parameters τ and c demonstrate pronounced sensitivity in scenario III. The outcomes derived from this method are distinctive and carry significant implications for the dynamics of optical fibers and wave phenomena across various optical systems.

Keywords: ( G ?/ G , 1/ G )-expansion method; exact solutions; Biswas–Milovic equation; Kerr and power law nonlinearity; optical soliton solutions; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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