A remark on the inverse scattering problem for the perturbed Hill equation

DOI10.1134/S0001434622070306OpenAlexW4293795028MaRDI QIDQ2170519

A. F. Mamedova, Agil K. Khanmamedov

Publication date: 6 September 2022

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434622070306

zbMATH Keywords

Hill equationJost solutionmethod of Riemann functiontriangular representation

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (2)

Transformation operator for the Schrödinger equation with additional exponential potential ⋮ TRIANGULAR REPRESENTATION OF THE JOST-TYPE SOLUTION TO THE PERTURBED MODIFIED MATHIEU EQUATION

Cites Work

• On the Riemann-Green function
• Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• An inverse scattering problem for a perturbed Hill's operator
• THE DIRECT AND INVERSE SCATTERING PROBLEMS FOR THE ONE-DIMENSIONAL PERTURBED HILL OPERATOR
• ON SOLUTION OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION WITH INITIAL DATA THE SUM OF A PERIODIC AND A RAPIDLY DECREASING FUNCTION

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