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

    Authors

    E. Sweet;R. A. Van Gorder

    Comments

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    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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