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

Research output: Working paper › Working paper and Preprints

17 Citations (Scopus)

227 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

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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http://hdl.handle.net/1983/250

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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",

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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 ",

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AU - Champneys, AR

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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

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