Direct and inverse scattering for selfadjoint Hamiltonian systems on the line
An inverse scattering theory is constructed for the selfadjoint system of differential equations \[ -iJ_{2n}Y'(x,\lambda)-V(x)Y(x,\lambda)=\lambda Y(x,\lambda),\quad -\infty<x<\infty, \] on the line, with \[ J_{2n}=\left[\begin{matrix} I_n & 0 \\ 0 & -I_n\end{matrix}\right],\qquad V(x)=\left[\begin{matrix} 0 & k(x) \\ k^*(x) & 0 \end{matrix}\right], \] \(I_n\) is the identity matrix of odd order \(n\), \(k(x)\in L(-\infty,\infty)\) is the \(n\times n\)-matrix function, and \(*\) denotes the matrix conjugate transpose.
scientific article; zbMATH DE number 1542407
scientific article