Abstract
This paper establishes that solitary waves for the generalized Korteweg–de Vries equation and for the generalized Boussinesq equation are stable if the flux function p satisfies p ″ > 0 and p ‴ ⩽ 0 . While p ″ > 0 alone suffices for the stability of waves of sufficiently small amplitude, obvious examples show that p ‴ ⩽ 0 cannot be omitted in the general case.
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