  The spacelike reduction of the Chern-Simons Lagrangian yields a modified
Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle
density is replaced by current. When the phase is linear in the position, this
latter is an ordinary NLS with time-dependent coefficients which admits
interesting solutions, whose arisal is explained by the conformal properties of
non-relativistic spacetime. However, only the usual travelling soliton is
consistent with the jNLS. Adding a six-order potential converts jnLS into an
integrable equation.
