Inverse scattering problem for a cubic string having the shape of a step

2025/09/08 by Vladimir A. Zolotarev, Zolotarev, Vladimir A.
Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Electromagnetic Scattering and Analysis #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2509.06417

openalex publication_date 2025/09/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``+∞'', and its dual, correspondingly, of the waves from ``-∞''. The main systems of linear singular equations for both problems are obtained. It is shown how to unambiguously restore potential from the solutions to these equation systems.

Citations

• Inverse scattering problem for third order differential operators on the whole axis
• Inverse scattering problem for a third-order operator with local potential
• A New Integrable Equation with Peakon Solutions

Related

• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class <i>ψ_xxx</i> + 6<i>Qψ_x</i> + 6<i>R_ψ</i> = λ<i>ψ</i>
• The cubic NLS on the line with an inverse square potential
• Stability of the solution to inverse obstacle scattering problem
• Discrete Multichannel Scattering with step-like potential
• Stability of solutions to inverse scattering problems with fixed-energy data