New exact solitary wave solutions for the 3D-FWBBM model in arising shallow water waves by two analytical methods

• Published in: Results in physics Vol. 25; p. 104230
• Main Authors: Shafqat-Ur-Rehman, Bilal, Muhammad, Ahmad, Jamshad
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2021; Elsevier
• Subjects: 3D-FWBBM equation; Conformable fractional derivative; Exact solitary wave structures; MDAM; The new Φ6-model expansion method; Exact solitary wave structures; 3D-FWBBM equation; The new Φ6-model expansion method; Conformable fractional derivative; MDAM
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104230

In this article, we investigate the exact solitary wave solutions to the 3D fractional Wazwaz-Benjamin- Bona-Mahony (3D-FWBBM) equation in emerging shallow-water waves. Different kinds of solutions such as hyperbolic, trigonometric, Jacobi elliptic, and rational function including some special known solitary waves like shock, singular, combo shock-solitary wave, and multiple soliton solutions are achieved by the utilization of the sound computational integration tools namely the new Φ6-model expansion method and modified direct algebraic method (MDAM). In addition, we also secure mixed combined solitons and singular periodic solutions and the constraint conditions also emerge which provide the guarantee to the reported solutions. Some results are figured out graphically in 3D, 2D, and their corresponding contour profiles by selecting appropriate parametric values to anticipate the wave dynamics of the solutions. The obtained outcomes are more general and fresh to show that these applied methods are concise, direct, elementary, and can be imposed in more complex phenomena with the assistance of symbolic computations. •The (3+1)-dimensional fractional Wazwaz-Benjamin-Bona-Mahony equation is consider.•We applied hydrodynamic mathematical methods.•Hyperbolic, dark, singular, periodic and combined soliton solutions are extracted.