Figure 3
We decompose the monodromy matrix into four parts \(M_{3} = M_{0} R_{0,x} M_{x} R_{0,x}^{ - 1}\), where matrices M0 and Mx encode the local phases that three solutions \(\left\{ {z^{s1,2,3} } \right\}\) and \(\left\{ {\left( {z - x} \right)^{s1,2,3} } \right\}\) obtain around \(z = 0\) and \(z = x\) respectively; while the “Scattering Matrix” \(R_{0,x}\) represents how the modes \(\left\{ {z^{s1,2,3} } \right\}\) scatter into the modes \(\left\{ {\left( {z - x} \right)^{s1,2,3} } \right\}\) as they “Propagate” via the differential Eq. (41) from near \(z = 0\) to near \(z = x\). We need to make the radii very small for this representation to be accurate.
