Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We prove the instability of a ``critical'' solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instability regions. The instability mechanism involved is ``purely nonlinear'', in the sense that the linearization at a critical soliton does not have eigenvalues with positive real part. We prove that critical solitons correspond generally to the saddle-node bifurcation of two branches of solitons.
Keywords
Cite
@article{arxiv.math/0609010,
title = {Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation},
author = {Andrew Comech and Scipio Cuccagna and Dmitry Pelinovsky},
journal= {arXiv preprint arXiv:math/0609010},
year = {2007}
}
Comments
34 pages, 3 figures