Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

Abstract

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt −uxx−uyy−(u2)xx−uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt −6ux 2 +6uuxx −uxxxx −uyy −uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

New Application of Differential Transformation Method for Improved Boussinesq Equation

“…In (Bratsos 2007), a predictor corrector (P-C) scheme is applied successfully to a nonlinear Boussinesq equation. Authors of (Wang 2008) discussed the improved and generalized Boussinesq equation and some other schemes are presented in (Yildirim 2011;Sariaydin 2010).…”