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On numerical soliton solution of the Kaup–Kupershmidt equation and convergence analysis of the decomposition method

Mustafa Inc
Organization: Firat University
Department: Department of Mathematics
Journal / Anthology

Applied Mathematics and Computation
Year: 2006
Volume: 172
Page range: 72-85

In this paper, we use the Adomian decomposition method (ADM) for obtaining soliton solution of the Kaup–Kupershmidt (KK) equation. We prove the convergence of this method applied to the nonlinear Kaup–Kupershmidt equation. The solution is found as an infinite series quickly converging to accurate solutions. The results of numerical examples are presented and only few terms are required to obtain accurate solutions. Most of the symbolic and numerical computations have been performed using the Computer Algebra System—Mathematica.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations