Akademik Veri Yönetim Sistemi
INVERSE PROBLEMS, cilt.41, sa.12, 2025 (SCI-Expanded, Scopus)
We consider the third-order linear differential equation d3 psi dx3+Q(x)d psi dx+P(x)psi=k3 psi,x is an element of R, where the complex-valued potentials Q and P are assumed to belong to the Schwartz class. We describe the basic solutions, the scattering coefficients, and the bound-state information, and we introduce the dependency constants and the normalization constants at the bound states. When the secondary reflection coefficients are zero, we provide a method to solve the corresponding inverse scattering problem, where the goal is to recover the two potentials Q and P from the scattering data set consisting of the transmission and primary reflection coefficients and the bound-state information. We formulate the corresponding inverse scattering problem as a Riemann-Hilbert problem on the complex k-plane and describe how the potentials are recovered from the solution to the Riemann-Hilbert problem. In the absence of bound states, we introduce a linear integral equation, which is the analog of the Marchenko integral equation used in the inverse scattering theory for the full-line Schr & ouml;dinger equation. We describe the recovery of the two potentials from the solution to the aforementioned linear integral equation.