Instability of a class of dispersive solitary waves. (English) Zbl 0713.35108

The authors consider the equation in \({\mathbb{R}}^ 2\), \(Mu_ t+f(u)_ x=0\), where M is a pseudo-differential operator with elliptic symbol m(\(\xi\)) of order \(\geq 1\). The stability and instability properties of solitary wave solutions g(x-ct) are studied in detail, and the obtained results are tested on some interesting examples. The equation \(u_ t- Mu_ x+f(u)_ x=0\) is then also considered.
Reviewer: L.Rodino


35S05 Pseudodifferential operators as generalizations of partial differential operators
35Q51 Soliton equations
35B35 Stability in context of PDEs
Full Text: DOI


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