A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation

Laura-Jane Louise Hattam; Simon Rex Clarke

doi:10.1016/j.wavemoti.2015.07.006

A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation

Laura-Jane Louise Hattam, Simon Rex Clarke

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

The stability of periodic solutions to the steady forced Korteweg–de Vries–Burgers (fKdVB) equation is investigated here. This family of periodic solutions was identified by Hattam and Clarke (2015) using a multi-scale perturbation technique. Here, Floquet theory is applied to the governing equation. Consequently, two criteria are found that determine when the periodic solutions are stable. This analysis is then confirmed by a numerical study of the steady fKdVB equation.

Original language	English
Pages (from-to)	42-51
Number of pages	10
Journal	Wave Motion
Volume	59
DOIs	https://doi.org/10.1016/j.wavemoti.2015.07.006
Publication status	Published - 2015

Keywords

Korteweg–de Vries
Stability
Floquet theory
Periodic solutions

Access to Document

10.1016/j.wavemoti.2015.07.006

Cite this

@article{236c2894ecc340cebbbf6c2394c16d1e,

title = "A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation",

abstract = "The stability of periodic solutions to the steady forced Korteweg–de Vries–Burgers (fKdVB) equation is investigated here. This family of periodic solutions was identified by Hattam and Clarke (2015) using a multi-scale perturbation technique. Here, Floquet theory is applied to the governing equation. Consequently, two criteria are found that determine when the periodic solutions are stable. This analysis is then confirmed by a numerical study of the steady fKdVB equation.",

keywords = "Korteweg–de Vries, Stability, Floquet theory, Periodic solutions",

author = "Hattam, {Laura-Jane Louise} and Clarke, {Simon Rex}",

year = "2015",

doi = "10.1016/j.wavemoti.2015.07.006",

language = "English",

volume = "59",

pages = "42--51",

journal = "Wave Motion",

issn = "0165-2125",

publisher = "Elsevier",

}

TY - JOUR

T1 - A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation

AU - Hattam, Laura-Jane Louise

AU - Clarke, Simon Rex

PY - 2015

Y1 - 2015

N2 - The stability of periodic solutions to the steady forced Korteweg–de Vries–Burgers (fKdVB) equation is investigated here. This family of periodic solutions was identified by Hattam and Clarke (2015) using a multi-scale perturbation technique. Here, Floquet theory is applied to the governing equation. Consequently, two criteria are found that determine when the periodic solutions are stable. This analysis is then confirmed by a numerical study of the steady fKdVB equation.

AB - The stability of periodic solutions to the steady forced Korteweg–de Vries–Burgers (fKdVB) equation is investigated here. This family of periodic solutions was identified by Hattam and Clarke (2015) using a multi-scale perturbation technique. Here, Floquet theory is applied to the governing equation. Consequently, two criteria are found that determine when the periodic solutions are stable. This analysis is then confirmed by a numerical study of the steady fKdVB equation.

KW - Korteweg–de Vries

KW - Stability

KW - Floquet theory

KW - Periodic solutions

UR - http://www.sciencedirect.com/science/article/pii/S0165212515001006/pdfft?md5=24850ea285e0f54ed6ddda9602919c55&pid=1-s2.0-S0165212515001006-main.pdf

U2 - 10.1016/j.wavemoti.2015.07.006

DO - 10.1016/j.wavemoti.2015.07.006

M3 - Article

SN - 0165-2125

VL - 59

SP - 42

EP - 51

JO - Wave Motion

JF - Wave Motion

ER -

A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation

Abstract

Keywords

Access to Document

Other files and links

Cite this