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

Laura Hattam

doi:10.1016/j.wavemoti.2015.07.006

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

Laura Hattam

Institute for Mathematical Innovation (IMI)

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

3 Citations (SciVal)

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
Early online date	3 Aug 2015
DOIs	https://doi.org/10.1016/j.wavemoti.2015.07.006
Publication status	Published - 1 Dec 2015

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10.1016/j.wavemoti.2015.07.006

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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.",

author = "Laura Hattam",

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AU - Hattam, Laura

PY - 2015/12/1

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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.

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

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