Exact one-species evolution

Let $q=B(1)$, $\eta =|q{|}^2$. Unitarity gives ${\Vert \psi (1)\Vert }^2=1-\eta$. Zero coupling gives $B=0$; if $v=\kappa =0$, $A(u)=g(u+1)$.

For the primary Volterra operator, the componentwise maximum-norm majorant is $1+|\kappa (u)|$. Thus

Ordered integration proves a uniformly convergent Neumann series, with truncation after $m$ bounded by $e^M{M}^{m+1}/(m+1)!$.