Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Authors:

• Mohamed M. Mousa
• Aidarkhan Kaltayev

Keywords:

• Homotopy perturbation method
• Padé approximants
• cubic Boussinesq equation
• modified Boussinesq equation.

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