  A quantisation of the KP equation on a cylinder is proposed that is
equivalent to an infinite system of non-relativistic one-dimensional bosons
carrying masses $m=1,2,\ldots$ The Hamiltonian is Galilei-invariant and
includes the split $\Psi^\dagger_{m_1}\Psi^\dagger_{m_2}\Psi_{m_1+m_2}$ and
merge $\Psi^\dagger_{m_1+m_2}\Psi_{m_1}\Psi_{m_2}$ terms for all combinations
of particles with masses $m_1$, $m_2$ and $m_1+m_2$, with a special choice of
coupling constants. The Bethe eigenfunctions for the model are constructed. The
consistency of the coordinate Bethe Ansatz, and therefore, the quantum
integrability of the model is verified up to the mass $M=8$ sector.
