We study a (1+1)-dimensional nonlinear Schrodinger equation, which is invariant under dilation and special conformal transformation, in addition to spacetime translations and Galileo boost. The behaviour of a soliton solution to this equation, in an external field which represents a linear repulsive or a harmonic restoring force, is investigated. Explicit solutions are presented. In the former case, the soliton will go to infinity, with its size increasing exponentially with time and, thus, finally collapse. In the latter case, the solution is periodic in time, showing that the soliton binds to the external force. The binding energy is quantized semiclassically by the Bohr-Sommerfeld procedure. In both cases, the centre of the soliton moves in the same way as a classical particle. The nonlinear term in this Schrodinger equation leads to a three-body contact interaction after second quantization. The quantum-mechanical three-body wave equation in configuration space is completely solved.