Scattering of Solitons in Derivative Nonlinear Schr\"{o}dinger Model

TL;DR

This paper demonstrates how to make a chiral soliton model integrable by adding a specific potential, deriving explicit soliton solutions, and connecting classical results to quantum mechanics in the weak coupling limit.

Contribution

It introduces a modified derivative nonlinear Schrödinger model with explicit soliton solutions and links classical and quantum properties.

Findings

Explicit one and two soliton solutions derived

Model becomes integrable with added potential

Classical solutions match quantum bound states in weak coupling

Abstract

We show that the chiral soliton model recently introduced by Aglietti et al. can be made integrable by adding an attractive potential with a fixed coefficient. The modified model is equivalent to the derivative nonlinear Schr\"{o}dinger model which does not possess parity and Galilean invariance. We obtain explicit one and two classical soliton solutions and show that in the weak coupling limit, they correctly reproduce the bound state energy as well as the time delay of two-body quantum mechanics of the model.