Optical Solutions of the Date–Jimbo–Kashiwara–Miwa Equation via the Extended Direct Algebraic Method. (26th July 2021)

• Record Type: Journal Article
• Authors: Akram, Ghazala; Sajid, Naila; Abbas, Muhammad; Hamed, Y. S.; M. Abualnaja, Khadijah
• Other Names: Akdemir Ahmet Ocak Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-07-26
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5591016
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : In this study, the solutions of 2 + 1 -dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation are characterized, which can be used in mathematical physics to model water waves with low surface tension and long wavelengths. The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions. The complex-valued solutions represent traveling waves in different structures, such as bell-, V-, and W-shaped multiwaves. The results obtained in this article are novel and more general than those contained in the literature (Wang et al., 2014, Yuan et al., 2017, Pu and Hu 2019, Singh and Gupta 2018). Furthermore, the mechanical features and dynamical characteristics of the obtained solutions are demonstrated by three-dimensional graphics.