A stability result for solitary waves in nonlinear dispersive equations

B Akers; Paul A Milewski

A stability result for solitary waves in nonlinear dispersive equations

B Akers
, Paul A Milewski

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

6 Citations (SciVal)

252 Downloads (Pure)

Abstract

The stability of solitary traveling waves in a general class of conservative nonlinear dispersive equations is discussed. A necessary condition for the exchange of stability of traveling waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and from a few integrable partial differential equations, to a broader class of conservative differential equations, with particular application to gravity-capillary surface waves.

Original language	English
Pages (from-to)	791-797
Number of pages	7
Journal	Communications in Mathematical Sciences
Volume	6
Issue number	3
Publication status	Published - Sept 2008

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Milewski_CommMathSci_6_3_791.pdf
© International Press. First published in Communications in Mathematical Sciences in volume 6, number 3, 2008, published by International Press.

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title = "A stability result for solitary waves in nonlinear dispersive equations",

abstract = "The stability of solitary traveling waves in a general class of conservative nonlinear dispersive equations is discussed. A necessary condition for the exchange of stability of traveling waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and from a few integrable partial differential equations, to a broader class of conservative differential equations, with particular application to gravity-capillary surface waves.",

author = "B Akers and Milewski, \{Paul A\}",

year = "2008",

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language = "English",

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T1 - A stability result for solitary waves in nonlinear dispersive equations

AU - Akers, B

AU - Milewski, Paul A

PY - 2008/9

Y1 - 2008/9

N2 - The stability of solitary traveling waves in a general class of conservative nonlinear dispersive equations is discussed. A necessary condition for the exchange of stability of traveling waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and from a few integrable partial differential equations, to a broader class of conservative differential equations, with particular application to gravity-capillary surface waves.

AB - The stability of solitary traveling waves in a general class of conservative nonlinear dispersive equations is discussed. A necessary condition for the exchange of stability of traveling waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and from a few integrable partial differential equations, to a broader class of conservative differential equations, with particular application to gravity-capillary surface waves.

UR - https://www.scopus.com/pages/publications/56349114397

UR - http://www.intlpress.com/CMS/2008/issue6-3/

M3 - Article

SN - 1539-6746

VL - 6

SP - 791

EP - 797

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

IS - 3

ER -

A stability result for solitary waves in nonlinear dispersive equations

Abstract

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