Stability of large- and small-amplitude solitary waves in the generalized Korteweg-de Vries and Euler-Korteweg/Boussinesq equations

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 satisfiesp″>0andp‴⩽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.