Abstract
The authors study the stability problem for bound states of (1+1)-dimensional scalar fields considering different definitions of stability. Sharp stability and instability conditions for Liapunov stability are established by improving the Shatah-Strauss formalism (1985) and a recent technique of Grillakis, Shatah and Strauss (1987) based on an analysis of the linearised operators. The linear dynamical stability is investigated for the first time and a sharp stability condition is obtained. Explicit results for the regimes of stability and instability are given for power-like self-interactions and for the phi 4- phi 6 model.
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