NONLINEAR SCHRODINGER SOLITONS IN THE PRESENCE OF AN EXTERNAL POTENTIAL

We study the influence of external potentials on the solitary wave solutions of certain nonlinear partial differential equations common in physics. Our approach allows for both the translation of pulse-like envelopes through space and the 'breathing' of these pulses in the centre-of-mass frame. We find that for certain simple potentials it is possible for the familiar soliton solutions of these equations to be preserved and to execute essentially classical motion. For more general potentials, however, we find that the familiar pulse shapes cannot be preserved; shape deformations more complex than our simple breathing motion are required. When shape deformations are not too severe, our approach allows an approximate solution for the case of adiabatic following.