Title

Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6

Authors

Authors

E. Sweet;R. A. Van Gorder

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Appl. Math. Comput.

Keywords

Drinfel'd-Sokolov equation; Analytical solution; Nonlinear PDE; HOMOTOPY ANALYSIS METHOD; NONLINEAR DIFFERENTIAL-EQUATIONS; TANH METHOD; W-ALGEBRAS; PERIODIC-SOLUTIONS; WILSON EQUATION; WAVE-EQUATIONS; REDUCTION; OPERATORS; EVOLUTION; Mathematics, Applied

Abstract

Analytical solutions to the generalized Drinfel'd-Sokolov (GDS) equations u(t) + alpha(1)uu(x) + beta(1)u(xxx) + gamma(v(delta))(x) = 0 and v(t) + alpha(2)uv(x) + beta(2)v(xxx) = 0 are obtained for various values of the model parameters. In particular, we provide perturbation solutions to illustrate the strong influence of the parameters beta(1) and beta(2) on the behavior of the solutions. We then consider a Miura-type transform which reduces the gDS equations into a sixth-order nonlinear differential equation under the assumption that delta = 1. Under such a transform the GDS reduces to the sixth-order Drinfel'd-Sokolov-Satsuma-Hirota (DSSH) equation (also known as KdV6) in the very special case alpha(1) = -alpha(2). The method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary alpha(1) and alpha(2). An error analysis of the obtained approximate analytical solutions is provided. (C) 2010 Elsevier Inc. All rights reserved.

Journal Title

Applied Mathematics and Computation

Volume

216

Issue/Number

10

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

2783

Last Page

2791

WOS Identifier

WOS:000278542800001

ISSN

0096-3003

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