= Sectorial half-line mKdV Riemann-Hilbert reconstruction
{title2=$\Sigma=\{k:\operatorname{Im}k^3=0\}$}
Use the bounded columns supplied by <Volterra analyticity sectors for reverse-dispersion mKdV> and divide the necessary columns by their determinants. This gives a normalized meromorphic matrix on the six-ray contour $\arg k=m\pi/3$. The constant <scattering data> connection matrices generate its jumps by conjugation with $e^{i(kx-4k^3t)\sigma_3}$. Zeros of column determinants require residue conditions; in a sufficiently small-data, zero-free regime only jumps are needed. The off-diagonal expansion coefficient reconstructs $q=-2i\lim_{k\to\infty}kM_{12}$ for this sign convention.
Back to article page
