Half-line NLS global relation
= Half-line NLS global relation
{title2=$A(k)b(k)-B(k)a(k)=e^{4ik^2T}c_T(k)$}
Evaluating the <Lax pair> connection formula at $(0,T)$ gives $S^{-1}s=e^{2ik^2T\widehat\sigma_3}\mu_3(0,T,k)$. The upper off-diagonal entry is the displayed relation, where $c_T=[\mu_3(0,T)]_{12}$ is analytic in the upper half-plane and is $O(1/k)$. A finite-time relation must retain this final-state term.