  We introduce and study an integrable boundary flow possessing an infinite
number of conserving charges which can be thought of as quantum counterparts of
the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact
expression for overlap amplitudes of the boundary state with all primary states
in terms of solutions of certain ordinary linear differential equation. The
boundary flow is terminated at a nontrivial infrared fixed point. We identify a
form of whole boundary state corresponding to this fixed point.
