  It is proved that the Lieb-Liniger (LL) cusp condition implementing the delta
function interaction in one-dimensional Bose gases is dynamically conserved
under phase imprinting by pulses of arbitrary spatial form and the subsequent
many-body dynamics in the thermodynamic limit is expressed approximately in
terms of solutions of the time-dependent single-particle Schrodinger equation
for a set of time-dependent orbitals evolving from an initial LL-Fermi sea. As
an illustrative application, generation of gray solitons in a LL gas on a ring
by a phase-imprinting pulse is studied.
