  This study aims to explore the complex interactions between an internal
solitary wave and an external force using the Benjamin-Ono equation as the
theoretical framework. The investigation encompasses both asymptotic and
numerical approaches. By assuming a small amplitude for the external force, we
derive a dynamical system that describes the behavior of the solitary wave
amplitude and the position of its crest. Our findings reveal three distinct
scenarios: (i) resonance between the solitary wave and the external force, (ii)
oscillatory motion with closed orbits, and (iii) displacement from the initial
position while maintaining the wave direction. However, through numerical
simulations, we observe a different relationship between the amplitude of the
solitary wave and its crest position. Specifically, for external forces of
small amplitude, the simulations indicate the presence of an unstable spiral
pattern. Conversely, when subjected to external forces of larger amplitudes,
the solitary wave exhibits a stable spiral trajectory which resembles the
classical damped mass-spring system.
