TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=56349114397&partnerID=8YFLogxK
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 -