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The Backscattering Problem for Time-Dependent Potentials
Medet Nursultanov1,2, Lauri Oksanen1, Plamen Stefanov3
1Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.
Annales Henri Poincare
|June 15, 2026
Summary
This study addresses the inverse backscattering problem for time-dependent potentials. Researchers proved uniqueness and Lipschitz stability for recovering small potentials.
Area of Science:
- Mathematical Physics
- Inverse Problems
Background:
- The inverse backscattering problem aims to determine potential functions from scattered wave data.
- Time-dependent potentials introduce complexities compared to static potentials.
Purpose of the Study:
- To investigate the inverse backscattering problem for time-dependent potentials.
- To establish theoretical guarantees for potential recovery.
Main Methods:
- Utilizing techniques from partial differential equations.
- Applying stability analysis to inverse scattering theory.
Main Results:
- Demonstrated uniqueness of solution for the inverse problem.
- Proved Lipschitz stability for the reconstruction of small potentials.
Conclusions:
- The findings provide a foundation for analyzing time-dependent inverse scattering problems.
- Guarantees of uniqueness and stability are crucial for practical applications in potential recovery.
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