Title

Asymptotic solutions for singularly perturbed Boussinesq equations

Authors

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

DOI Link

http://dx.doi.org/10.1016/j.amc.2012.04.001

Language

English

First Page

10238

Last Page

10243

WOS Identifier

WOS:000303982000022

ISSN

0096-3003

Recommended Citation

"Asymptotic solutions for singularly perturbed Boussinesq equations" (2012). Faculty Bibliography 2010s. 2727.
https://stars.library.ucf.edu/facultybib2010/2727