NONLINEAR SCHRODINGER SOLITONS IN THE PRESENCE OF AN EXTERNAL POTENTIAL

We study the influence of external potentials on the solitary wave sol utions of certain nonlinear partial differential equations common in p hysics. Our approach allows for both the translation of pulse-like env elopes through space and the 'breathing' of these pulses in the centre -of-mass frame. We find that for certain simple potentials it is possi ble for the familiar soliton solutions of these equations to be preser ved and to execute essentially classical motion. For more general pote ntials, however, we find that the familiar pulse shapes cannot be pres erved; shape deformations more complex than our simple breathing motio n are required. When shape deformations are not too severe, our approa ch allows an approximate solution for the case of adiabatic following.