Novel waves structures for two nonlinear partial differential equations arising in the nonlinear optics via Sardar-subequation method

Naeem Ullah; Muhammad Imran Asjad; Abid Hussanan; Ali Akgül; Wedad R. Alharbi; H. Algarni; I.S. Yahia

Alexandria Engineering Journal (May 2023)

Novel waves structures for two nonlinear partial differential equations arising in the nonlinear optics via Sardar-subequation method

Naeem Ullah,
Muhammad Imran Asjad,
Abid Hussanan,
Ali Akgül,
Wedad R. Alharbi,
H. Algarni,
I.S. Yahia

Affiliations

Naeem Ullah: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Muhammad Imran Asjad: Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Abid Hussanan: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54000, Pakistan
Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey; Corresponding author at: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
Wedad R. Alharbi: Physics Department, College of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
H. Algarni: Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Sci-ence, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
I.S. Yahia: Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Sci-ence, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia; Center of Medical and Bio-Allied Health Sciences Research (CMBHSR), Ajman University, Ajman P.O. Box 346, United Arab Emirates; Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Semiconductor Lab., Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt

Journal volume & issue: Vol. 71
pp. 105 – 113

Abstract

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In this paper, our aim is to construct the novel wave structures for two non-linear evolution equations which are rising in non-linear optics, mathematical biological models, fluid dynamics, waves theory, mechanics, quantum mechanics, and many more. We employed an efficient analytical technique namely, the Sardar-subequation method to build the wave solutions for the modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations. We have built the numerous type of soliton wave structures of modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations via the Sardar-subequation method. Acquired results reveal the dynamics behavior of waves structures including the bright, singular, dark, and periodic singular solitons solutions. To illustrate the behavior of these solutions some selected solutions are sketched in two-, and three-dimensional graphs. On the basis of these results, our technique is suitable, up-to-date, and powerful. The obtained solutions are very efficacious and influential in non-linear optics, mathematical biology, mechanics, fluid mechanics, plasma physics, and many more. This study will assist to predict some new hypothesis and theories in the field of mathematical physics.

Published in Alexandria Engineering Journal

ISSN: 1110-0168 (Print); 2090-2670 (Online)
Publisher: Elsevier
Country of publisher: Egypt
LCC subjects: Technology: Engineering (General). Civil engineering (General)
Website: http://www.journals.elsevier.com/alexandria-engineering-journal/

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