2021/12/29 by N. A. Khokhlov, Khokhlov, N. A.
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Photorefractive and Nonlinear Optics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2112.14342
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a generalization of the algebraic method for solving the Marchenko equation (fixed-l inversion) for any values of the orbital angular momentum l. We expand the Marchenko equation kernel in a separable form using a triangular wave set. The separable kernel allows a reduction of the equation to a system of linear equations. We obtained a linear expression of the kernel expansion coefficients in terms of the Fourier series coefficients of q(1-S(q)) function (S(q) is the scattering matrix) depending on the momentum q. The linear expression is valid for any orbital angular momentum l. The kernel expansion coefficients are determined by the scattering data in the finite range 0≤ q≤π/h. In turn, the thus defined Marchenko kernel of the equation allows one to find the potential function of the radial Schrödinger equation with h-step accuracy.