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Zbl 1065.35219
Kaya, Doǧan; El-Sayed, Salah M.
Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method. (English)
[J] Phys. Lett., A 320, No. 2-3, 192-199 (2003). ISSN 0375-9601

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 2000:: *35Q53 KdV-like equations
35Q51 Solitons
65M99 Numerical methods for IVP of PDE

Keywords: Adomian decomposition method; initial conditions; convergence

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Zentralblatt MATH Berlin [Germany]