On the stability of solitary wave solutions of the 5th-order KdV equation

AV Buryak; AR Champneys

doi:10.1016/S0375-9601(97)00453-2

On the stability of solitary wave solutions of the 5th-order KdV equation

AV Buryak, AR Champneys

Systems Centre

Research output: Working paper

22 Citations (Scopus)

370 Downloads (Pure)

Abstract

The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky [Physica D, 3 (1981) 428-438] that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results

Original language	English
Publisher	University of Bristol
Number of pages	6
DOIs	https://doi.org/10.1016/S0375-9601(97)00453-2
Publication status	Published - Oct 1996

Bibliographical note

Additional information: Later published by Elsevier Science, (1997) Physics Letters A, 233 (1-2), pp. 58-62. ISSN 0375-9601

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

asymptotic theory
Korteweg-de Vries equation
multi-pulsed stationary solitary wave solutions
gravity-capillary water waves
fifth-order-derivative dispersive perturbation
Gorshkov and Ostrovsky
two-pulses

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10.1016/S0375-9601(97)00453-2

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On the stability of solitary wave solutions of the 5th-order KdV equation
Buryak, A. & Champneys, A., Oct 1996, University of Bristol, 6 p.
Research output: Working paper

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22 Citations (Scopus)

370 Downloads (Pure)

Cite this

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title = "On the stability of solitary wave solutions of the 5th-order KdV equation",

abstract = "The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky [Physica D, 3 (1981) 428-438] that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results",

keywords = "asymptotic theory, Korteweg-de Vries equation, multi-pulsed stationary solitary wave solutions, gravity-capillary water waves, fifth-order-derivative dispersive perturbation, Gorshkov and Ostrovsky, two-pulses",

author = "AV Buryak and AR Champneys",

note = "Additional information: Later published by Elsevier Science, (1997) Physics Letters A, 233 (1-2), pp. 58-62. ISSN 0375-9601 ",

year = "1996",

month = oct,

doi = "10.1016/S0375-9601(97)00453-2",

language = "English",

publisher = "University of Bristol",

address = "United Kingdom",

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T1 - On the stability of solitary wave solutions of the 5th-order KdV equation

AU - Buryak, AV

AU - Champneys, AR

N1 - Additional information: Later published by Elsevier Science, (1997) Physics Letters A, 233 (1-2), pp. 58-62. ISSN 0375-9601

PY - 1996/10

Y1 - 1996/10

N2 - The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky [Physica D, 3 (1981) 428-438] that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results

AB - The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave solutions. Here it is argued based on the asymptotic theory of Gorshkov and Ostrovsky [Physica D, 3 (1981) 428-438] that half of the two-pulses are stable. Comparison with numerically obtained two-pulses shows that the asymptotic theory is remarkably accurate, and time integration of the full partial differential equations confirms the stability results

KW - asymptotic theory

KW - Korteweg-de Vries equation

KW - multi-pulsed stationary solitary wave solutions

KW - gravity-capillary water waves

KW - fifth-order-derivative dispersive perturbation

KW - Gorshkov and Ostrovsky

KW - two-pulses

U2 - 10.1016/S0375-9601(97)00453-2

DO - 10.1016/S0375-9601(97)00453-2

M3 - Working paper

BT - On the stability of solitary wave solutions of the 5th-order KdV equation

PB - University of Bristol

ER -

On the stability of solitary wave solutions of the 5th-order KdV equation

Abstract

Bibliographical note

Research Groups and Themes

Keywords

Access to Document

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Research output

On the stability of solitary wave solutions of the 5th-order KdV equation

Cite this