Title

Asymptotic Solutions For Singularly Perturbed Boussinesq Equations

Keywords

Asymptotic series; Rational solutions; Singularly perturbed Boussinesq equation; Weak solutions

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. © 2012 Elsevier Inc. All rights reserved.

Publication Date

6-15-2012

Publication Title

Applied Mathematics and Computation

Volume

218

Issue

20

Number of Pages

10238-10243

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.amc.2012.04.001

Socpus ID

84861189318 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84861189318

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