Asymptotic solutions for singularly perturbed Boussinesq equations

    Authors

    J. Haussermann;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Singularly perturbed Boussinesq equation; Weak solutions; Rational; solutions; Asymptotic series; SHALLOW-WATER EQUATION; Mathematics, Applied

    Abstract

    We consider a family of singularly perturbed Boussinesq equations. We obtain a rational weak solution to the classical Boussinesq equation and demonstrate that this solution can be used to construct perturbation solutions for singularly perturbed high-order Boussinesq equations. These solutions take the form of an algebraic function which behaves similarly to a peakon, and which decays as time becomes large. We show that approximate solutions obtained via perturbation for the singularly perturbed models are asymptotic to the true solutions as the residual errors rapidly decay away from the origin. Published by Elsevier Inc.

    Journal Title

    Applied Mathematics and Computation

    Volume

    218

    Issue/Number

    20

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    10238

    Last Page

    10243

    WOS Identifier

    WOS:000303982000022

    ISSN

    0096-3003

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