Abstract
A second-order ordinary differential equation, which is a reduced form of the periodically forced extended Korteweg-de Vries (eKdV) equation, is derived in the physical context of sloshing a two-layer fluid tank. In the limit of small dispersion, numerical evidence is given of multiple periodic solutions displaying fast oscillations superimposed on slow periodic waves and a higher-order Melnikov method is then used to verify the existence of such solutions. The dynamical behaviour of a similar equation with more general coefficients is also examined, demonstrating the existence of periodic and chaotic behaviour. We highlight new aspects which arise due to the presence of mixed nonlinearity.
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