Abstract
In this paper, we employ the idea of homotopy perturbation transform method(HPTM), which is a combination of Laplace transformation and homotopy perturbation method(HPM) for solving nonlinear ordinary and partial differential equations. The equations are Laplace transformed and nonlinear terms are represented by He’s polynomials. The solutions are obtained in the series form which converges at fast rate with easily computable terms. Comparison of standard perturbation method shows that HPTM is appropriate even for system without any small/large parameters and therefore it can be applied more extensively than traditional perturbation techniques. HPTM is used to obtain soliton solution of Kaup-kupershimdt(KK) equation, which is modified form of fifth order KdV equation. Numerical results are presented in tabular form to show the accuracy, efficiency and reliability of this method.
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