Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions

Ismael, Hajar F.; Akkilic, Ayse Nur; Murad, Muhammad Amin Sadiq; Mahmoud, Walaa H.; Osman, M. S.

doi:10.1007/s11071-022-07817-5

Cited by 31 publications

(4 citation statements)

References 43 publications

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“…The variable coefficient nonlinear evolution equations (NLEEs) have become a pivotal and intricate realm of mathematical investigation, which forms a dynamic bridge between theoretical exploration and the intricacies of real-world phenomena 1 , 2 . These equations with variable coefficients play a vital role in modeling a wide array of natural systems, as they encapsulate the nuances that constant coefficients fail to capture 3 , 4 .…”

Section: Introductionmentioning

confidence: 99%

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics

Kawser,

Akbar,

Khan

et al. 2024

Sci Rep

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This article effectively establishes the exact soliton solutions for the Boussinesq model, characterized by time-dependent coefficients, employing the advanced modified simple equation, generalized Kudryashov and modified sine–Gordon expansion methods. The adaptive applicability of the Boussinesq system to coastal dynamics, fluid behavior, and wave propagation enriches interdisciplinary research across hydrodynamics and oceanography. The solutions of the system obtained through these significant techniques make a path to understanding nonlinear phenomena in various fields, surpassing traditional barriers and further motivating research and application. Significant impacts of the coefficients of the equation, wave velocity, and related parameters are evident in the profiles of soliton-shaped waves in both 3D and 2D configurations when all these factors are treated as variables, which are not seen in the case for constant coefficients. This study enhances the understanding of the significant role played by nonlinear evolution equations with time-dependent coefficients through careful dynamic explanations and detailed analyses. This revelation opens up an interesting and challenging field of study, with promising insights that resonate across diverse scientific disciplines.

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Section: Introductionmentioning

confidence: 99%

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics

Kawser,

Akbar,

Khan

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Conversely, analytical approximation techniques are preferred by scientists because they have deeper physical roots and are more deserving of parametric investigation. As a result, many researchers developed various methodologies, including the modified extended direct algebraic scheme 23 , Hirota Bilinear strategy 24 , Elzaki transform 25 , simple equation approach 26 , F -expansion scheme 27 , the extended Fan sub-equation strategy 28 , Natural Transform 29 , 30 , -expansion approach 31 , Darboux transformation scheme 32 , inverse scattering approach 33 , sardar equation method 34 , -Gorden equation approach 35 , and some others 36 – 43 .…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

Ahmad

Akram

Noor

et al. 2023

Sci Rep

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In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation approach and the improved F-expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Also, the stability of the outcomes is effectively examined. Several graphs have been sketched under appropriate parametric values to reinforce some reported findings. Computational work along with a graphical demonstration confirms the exactness of the proposed methods. The issue has not previously been investigated by taking into account the impact of the third order dispersion parameter. The main objective of this study is to obtain the different kinds of traveling wave solutions of fractional extended NLSE which are absent in the literature which justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of nonlinear sciences and optical engineering because these solutions will enables a through understanding of the development and dynamic nature of such models. The obtained results indicate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable traveling wave solutions to nonlinear equations emerging in various branches of scientific, technological, and engineering domains.

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“…To deal with this issue, several nonlinear terms should be considered, for example, the self-steepening, self-frequency shift, and non-Kerr nonlinearity, and so on. As a consequence, several new nonlinear equations were proposed [4,5,6,7,8,9,10], including several high-dimensional equations [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Novel solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary condition

Qiu

Zhang

2023

Nonlinear Dyn

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We present a determinant representation of generalized Darboux transformation for a generalized mixed nonlinear Schrödinger equation, and obtain several novel solutions with non-zero boundary condition. A complete classification of first-order solution with non-zero boundary condition is considered, and several second-order solutions, including some interesting structures, are discussed. Furthermore, by selecting special parameters in the equation, several novel kinds of solutions for the equation are displayed. Finally, we discuss the effects of parameter β, representing quintic nonlinearity term, on the breather solutions.

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Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions

Cited by 31 publications

References 43 publications

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics

Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

Novel solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary condition

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