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Additional solitonic and other analytical solutions for the higher-order Boussinesq-Burgers equation

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Abstract

Due to the lack of abundant literature with regard to the exact analytical solutions for the new higher-order Boussinesq-Burgers equations (HOBBE); of course, with the exception of a few that deployed the Hirota bilinear and ansatz methods, respectively, the present study is thus compelled to unravel more on the admissibility of additional exact solutions by the model through the application of Kudryashov method and exponential function expansion approach. In addition, the study equally proceeded by seeking the help of computer program for the computational as well the graphical visualizations. Amazingly, some important solitonic and other analytical solutions are acquired and examined via 2D and 3D depictions. Besides, the study further affirmed the acquired exponential function solution with the assistance of the novel exponential ansatz method. Indeed, the present study sheds more light on the dynamicity of the propagation of waves in the governing coupled nonlinear models, and by extension, it would pave the way for more revelations in the pulsation of waves in coupled higher-order evolution equations amidst various nonlinearities.

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Acknowledgements

The researcher would like to acknowledge Deanship of Scientific Research, Taif University for funding this work.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Collage of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    Ali M. Mubaraki

  2. Department of Mathematics, Faculty of Science, Federal University Dutse, Dutse, Jigawa State, Nigeria

    R. I. Nuruddeen

  3. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt

    Khalid K. Ali

  4. Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, C.P. 62209, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

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  1. Ali M. Mubaraki
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  2. R. I. Nuruddeen
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  3. Khalid K. Ali
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  4. J. F. Gómez-Aguilar
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Contributions

Ali M. Mubaraki: Conceptualization, Methodology, Writing- Original draft preparation, Software; R.I. Nuruddeen: Conceptualization, Methodology, Software, Writing-Original draft preparation; Khalid K. Ali: Methodology, Software, Writing-Original draft preparation; J.F. Gómez Aguilar: Conceptualization, Methodology, Writing- Original draft preparation, Software, Supervision. All authors read and approved the final manuscript.

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Correspondence to R. I. Nuruddeen or J. F. Gómez-Aguilar.

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Mubaraki, A.M., Nuruddeen, R.I., Ali, K.K. et al. Additional solitonic and other analytical solutions for the higher-order Boussinesq-Burgers equation. Opt Quant Electron 56, 165 (2024). https://doi.org/10.1007/s11082-023-05744-2

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