Phenomenological quantization scheme in a nonlinear Schroumldinger equation.

Abstract

A phenomenological quantization scheme is carried out for the collision process of identical solitons of a nonlinear Schr\"odinger equation. An effective potential is determined from the classical expression for the time delay. The corresponding effective $S$ matrix reproduces the exact $S$ matrix of the quantized nonlinear field as well as the ground-state binding energy for large $N$, but it is not adequate to describe the scattering process in the low-energy region.