Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Anjan Biswas; Jose Vega-Guzman; Anupma Bansal; Abdul H. Kara; Maggie Aphane; Yakup Yıldırım; Hashim M. Alshehri

doi:10.3176/proc.2023.1.03

Proceedings of the Estonian Academy of Sciences (Jan 2023)

Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Anjan Biswas,
Jose Vega-Guzman,
Anupma Bansal,
Abdul H. Kara,
Maggie Aphane,
Yakup Yıldırım,
Hashim M. Alshehri

Affiliations

Anjan Biswas: Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-4900, USA; Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca St., 800201 Galati, Romania; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa
Jose Vega-Guzman: Department of Mathematics, Lamar University, Beaumont, TX 77710, USA
Anupma Bansal: Department of Mathematics, D. A. V. College for Women, Ferozepur 152001, India
Abdul H. Kara: School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
Maggie Aphane: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa
Yakup Yıldırım: Department of Mathematics, Faculty of Arts and Sciences, Near East University, 99138 Nicosia, Cyprus
Hashim M. Alshehri: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

DOI: https://doi.org/10.3176/proc.2023.1.03
Journal volume & issue: Vol. 72, no. 1
pp. 17 – 29

Abstract

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This paper secures solitary waves, shock waves and singular solitary waves for the Boussinesq equation, which is studied with the inclusion of surface tension. The method of undetermined coefficients has yielded such waves. The Lie symmetry analysis has introduced a fresh perspective to the model. Conserved densities and corresponding conserved quantities are computed using the multiplier approach.

Published in Proceedings of the Estonian Academy of Sciences

ISSN: 1736-6046 (Print); 1736-7530 (Online)
Publisher: Estonian Academy Publishers
Country of publisher: Estonia
LCC subjects: Science
Website: https://eap.ee/proceedings/

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