Open Access
September 2008 A stability result for solitary waves in nonlinear dispersive equations
Benjamin Akers, Paul A. Milewski
Commun. Math. Sci. 6(3): 791-797 (September 2008).


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.


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Benjamin Akers. Paul A. Milewski. "A stability result for solitary waves in nonlinear dispersive equations." Commun. Math. Sci. 6 (3) 791 - 797, September 2008.


Published: September 2008
First available in Project Euclid: 29 September 2008

zbMATH: 1149.76022
MathSciNet: MR2455477

Primary: 76B15 , 76B25 , 76B45

Keywords: gravity-capillary wave , solitary wave , stability

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 3 • September 2008
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