INTERACTION OF A SOLITARY WAVE WITH AN EXTERNAL FORCE MOVING WITH VARIABLE-SPEED

The interaction of a solitary wave with an external force moving with constant acceleration is studied within the forced Korteweg-de Vries e quation. For the case of a weak isolated force an asymptotic model bas ed on equations for the amplitude and position of the solitary wave is developed. Phase portraits for this asymptotic system are obtained an alytically and numerically, Analysis has shown that an accelerated for ce of either sign can capture a solitary wave if the acceleration is l ess than a certain critical value, depending on the forcing amplitude (for the case of a constant force speed only a positive force can capt ure a solitary wave). Direct numerical simulation of the forced Kortew eg-de Vries equation has confirmed the predictions of the asymptotic m odel. Also, it is shown numerically that the accelerated force can cap ture more than one solitary wave.