The Propagating Exact Solitary Waves Formation of Generalized Calogero–Bogoyavlenskii–Schiff Equation with Robust Computational Approaches

Author:

Al Alwan Basem1,Abu Bakar Muhammad2,Faridi Waqas Ali2ORCID,Turcu Antoniu-Claudiu3ORCID,Akgül Ali456ORCID,Sallah Mohammed78ORCID

Affiliation:

1. Department of Chemical Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia

2. Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan

3. Department of Electrical Energy and Management, Faculty of Electrical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

4. Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon

5. Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey

6. Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Mersin 10, Nicosia 99138, Turkey

7. Applied Mathematical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

8. Higher Institute of Engineering and Technology, New Damietta 34517, Egypt

Abstract

The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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