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An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. (English) Zbl 1024.65096
Summary: By considering the Adomian decomposition method, explicit and numerical solutions are calculated for a various fifth-order Korteweg-de Vries (KdV) equations with initial condition. The method does not need linearization or weak nonlinearity assumptions, perturbation theory. The decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self-canceling “noise” terms where sum of components vanishes in the limit.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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