Communications in Mathematical Sciences
Volume 6 (2008)
A stability result for solitary waves in nonlinear dispersive equations
Pages: 791 – 797
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.
stability; solitary wave; gravity-capillary wave
2010 Mathematics Subject Classification
76B15, 76B25, 76B45