Nonlinear Dynamics

, Volume 88, Issue 4, pp 3017–3021 | Cite as

Solving the \(\mathbf{(3+1) }\)-dimensional KP–Boussinesq and BKP–Boussinesq equations by the simplified Hirota’s method

  • Abdul-Majid Wazwaz
  • S. A. El-Tantawy
Original Paper


We study two (3\(+\)1)-dimensional generalized equations, namely the Kadomtsev–Petviashvili–Boussinesq equation and the B-type Kadomtsev–Petviashvili–Boussinesq equation. We use the simplified Hirota’s method to conduct this study and to find the general phase shift of these equations. We obtain one- and two-soliton solutions, for each equation, with the coefficients of the three spatial variables are left as free parameters. However, we also develop special conditions on the coefficients of the spatial variables guarantee the existence of three-soliton solutions for each of these two equation.


Generalized KP equation BKP equation Boussinesq equation Simplified Hirota’s method 


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA
  2. 2.Department of Physics, Faculty of SciencePort Said UniversityPort SaidEgypt

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