Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method

E.J. Parkes; S. Abbasbandy

doi:10.1002/num.20348

Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method

E.J. Parkes, S. Abbasbandy

Mathematics And Statistics

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6 Citations (Scopus)

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Abstract

The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves.

Original language	English
Pages (from-to)	401-408
Number of pages	9
Journal	Numerical Methods for Partial Differential Equations
Volume	25
Issue number	2
DOIs	https://doi.org/10.1002/num.20348
Publication status	Published - 2009

Keywords

short-pulse equation
homotopy analysis method
solitary-wave solution
series solution

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10.1002/num.20348

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abstract = "The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves.",

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AB - The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves.

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KW - homotopy analysis method

KW - solitary-wave solution

KW - series solution

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JF - Numerical Methods for Partial Differential Equations

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