Ruhl, Joanna — Lagrange bracket approach to quantum fluctuations in macroscopic parameters of NLS breathers

In the focusing nonlinear Schrodinger equation, multisoliton ”breathers” may be created from a single mother soliton by quenching the strength of the nonlinear interaction. In ultracold-gas realizations, atop the mother soliton there are quantum fluctuations coming from its underlying quantum many-body nature, computable from the Bogoliubov theory. Post-quench, these fluctu- ations become the fluctuations in the macroscopic parameters of the daughters, which exist in a coherent macroscopic quantum state. We present a mean-field formalism that uses Lagrange brack- ets to compute, from given pre-quench fluctuations, the fluctuations of the macroscopic parameters of the daughter solitons, with results for both the 2-soliton and 3-soliton breathers.