2022/03/05 by T. Aktosun, Aktosun, T., R. Ercan +1 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #34A55 #34L25 #34L40 #47A40 #FOS: Mathematics #FOS: Physical sciences #Magneto-Optical Properties and Applications #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum optics and atomic interactions #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2203.02663
openalex publication_date 2022/03/05 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral equations is derived in such a way that the method can be applied to some other linear systems for which a Marchenko method is not yet available. It is shown how the potentials and the scattering solutions to the linear system are constructed from the solution to the Marchenko system. The bound-state information for the linear system with any number of bound states and any multiplicities is described in terms of a pair of constant matrix triplets. When the potentials in the linear system are reflectionless, some explicit solution formulas are presented in closed form for the potentials and for the scattering solutions to the linear system. The theory is illustrated with some explicit examples.