Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Ioannis Kourakis; Sharmin Sultana; Frank Verheest

doi:10.1007/s10509-011-0958-5

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Ioannis Kourakis
, Sharmin Sultana
, Frank Verheest

Mathematics

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

55 Scopus citations

Abstract

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Original language	British English
Pages (from-to)	245-249
Number of pages	5
Journal	Astrophysics and Space Science
Volume	338
Issue number	2
DOIs	https://doi.org/10.1007/s10509-011-0958-5
State	Published - Apr 2012

Keywords

Plasmas
Shock waves

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10.1007/s10509-011-0958-5

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title = "Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation",

abstract = "The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.",

keywords = "Plasmas, Shock waves",

author = "Ioannis Kourakis and Sharmin Sultana and Frank Verheest",

note = "Funding Information: Acknowledgements I.K. and S.S. acknowledge funding from the UK EPSRC (Engineering and Physical Science Research Council) via a Science and Innovation award to Centre for Plasma Physics, Queen{\textquoteright}s University Belfast (grant No. EP/D06337X/1).",

year = "2012",

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doi = "10.1007/s10509-011-0958-5",

language = "British English",

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pages = "245--249",

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AU - Kourakis, Ioannis

AU - Sultana, Sharmin

AU - Verheest, Frank

N1 - Funding Information: Acknowledgements I.K. and S.S. acknowledge funding from the UK EPSRC (Engineering and Physical Science Research Council) via a Science and Innovation award to Centre for Plasma Physics, Queen’s University Belfast (grant No. EP/D06337X/1).

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N2 - The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

AB - The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

KW - Plasmas

KW - Shock waves

UR - https://www.scopus.com/pages/publications/84857796435

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DO - 10.1007/s10509-011-0958-5

M3 - Article

AN - SCOPUS:84857796435

SN - 0004-640X

VL - 338

SP - 245

EP - 249

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

IS - 2

ER -

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Abstract

Keywords

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