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Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method. (English) Zbl 1065.35219
Summary: In this letter we present an Adomian’s decomposition method (ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
65M99Numerical methods for IVP of PDE