Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation
Articles > Article · 2010
Authors: Selin SARIAYDIN, Ahmet YILDIRIM
Zeitschrift für Naturforschung A, Journal Indexed in SCI Expanded, International, WoS, 2010, vol 65, pp 411-417
Summary
In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation u tt −u xx −u yy −(u 2 ) xx −u xxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation u xt −6u x 2 +6uu xx −u xxxx −u yy −u zz = 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.