Solitary wave structures of a family of 3D fractional WBBM equation via the tanh–coth​ approach

Abstract

The fractional nonlinear partial differential equation (FNLPDE), such as the family of 3D fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations, are investigated in this work. We engage the tanh–coth method for this family of FNLPDE to obtain different types of solitary wave solutions such as soliton, lump, kink, and traveling wave solutions with the assistance of MATLAB and Mathematica. Using the traveling wave transformation, the given FNLPDE turns into an ODE. Applying the auxiliary equation from the described method, we get an algebraic polynomial of ∅, compeering the like power to zero, we get a system of algebraic equations (SAE). Explaining the SAEs, we acquire the solutions sets for the constants. Expending the solutions to the ODE, we obtain the required solutions.

Keywords

• The tanh–coth method
• Wazwaz–Benjamin–Bona–Mahony​ equation
• Exact solution
• Solitary wave
• Soliton shape
• Lump shape