The dynamical behaviour of a reduction of the forced (and damped) Korteweg-de Vries equation is studied numerically. Chaos arising from subharmonic instability and homoclinic crossings are observed. Both period-doubling bifurcations and the Melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour, here characterised by a positive Lyapunov exponent. Supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits, and their behaviour under perturbation using Melnikov functions.
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Grimshaw et al. (1994) studied this question.
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