Instability of a class of dispersive solitary waves

Abstract

SynopsisThis paper studies the stability and instability properties of solitary wave solutions φ(x – ct) of a general class of evolution equations of the form Muttf(u)x=0, which support weakly nonlinear dispersive waves. It turns out that, depending on their speed c and the relation between the dispersion (i.e. the order of the pseudodifferential operator) and the nonlinearity, travelling waves maybe stable or unstable. Sharp conditions to that effect are given.