A variety of novel closed‐form soliton solutions to the family of Boussinesq‐like equations with different types

Kumar, Dipankar; Paul, Gour Chandra; Seadawy, Aly R.; Darvishi, M. T.

doi:10.1016/j.joes.2021.10.007

Cited by 14 publications

(1 citation statement)

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“…Numerous researchers have developed various methodologies to derive precise solutions for NLSEs, employing diverse approaches such as the G ′ G ′ +G+A method [7,8], the Sardar subequation method [9,10], the Riccati equation method [11,12], the Hirota bilinear method [13,14], the Lie group method [15,16], the (G ′ /G)-expansion technique [17,18], the extended Jacobi elliptic function method [19,20], the functional variable technique [21,22], the homogeneous balance method [23,24], the Hirota bilinear formulation with N-soliton [25,26], the new auxiliary equation method [27,28], the tanh-function method [29][30][31], the tanh-coth method [32,33], the generalized Kudryshov method [34,35], the exp(−φ(ξ)) -expansion method [36,37], the unified method [38,39], the multiple exp-function method [40,41] and so on.…”

Section: Introductionmentioning

confidence: 99%

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

Hossain,

Alsharif,

Miah

et al. 2024

Mathematics

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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.

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