Analytical and numerical solutions for the variant Boussinseq equations

Abstract

The principal objective of this paper is to employ the $\exp (-f(\zeta )) $-expansion and the adaptive moving mesh methods to express the exact travelling wave solutions and the numerical solutions, respectively, for the variant Boussinseq equations. Hyperbolic tangent and cotangent functions are utilized to build the exact solutions. The used numerical method uses the finite differences to discretize the proposed equations. The obtained numerical results are compared with other results obtained using the uniform mesh method. The achieved results show that both solutions match with each other. We also illustrate some 2D and 3D figures to confirm the validity of the numerical approach applied here.

Keywords

• variant boussinseq equations
• adaptive moving mesh equation
• travelling wave solution
• mmpdes
• monitor function
• $\exp (-f(\eta )) $-expansion method